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I Solving Equations by Adding or Subtracting ..:'II. Ouaf/tnt : How <on you u .. or 1Ub:'Klion to .. <01 •• equatio",! Obl«rl". Sol •• cnHlep equation. in one ... jabl. by u<i r>g addit i on or ,ublrKtion. equ. tion soIu!;"" of an equllion '1M hU a1!' Solution. .,. sometime'! written in a ""lIlion ... r. F e, Example lA, 'M solution .. ' i. (1 4). For example lB, the ",Iution •• !! ;'{H. Who "HI thlsl Athlete. C an an equat ion to estimat e their ma xi mum he an ral"" (See E .. mpl. 4 .) An "'l ua.; on is. 'hot OW<) expressions areequaJ. It ..,hnlon of an equation is a value of 'he v.riable lila! makes 'he equalionlrue. To find solution •. lIa1iabie. It variable is isol.ted when it apP'!ars by i'self on side of an equation, and not ., all on lhe olher side. lsolale a variable by using i"verse opemlion •. which ·undo· ope .. lions on the variab le. An equation is li ke a balanced scale. To keep the balarlce. I nv_ Oper.tlons perform the same operation Add x. _ Subtract x. on both s kie s. j j t t Solving Equations by Using Addition Solve eaoh equallon. x- 10_4 x-IO . 4 -±...!.I!. + 10 x .. 14 Chl!Ck x - 10 4 14 - 10 1' , " t .. m-t i ," m-t +.1 + .1 , , t- m Vr><e ro i. 'UbrrKfe<f from ;(. _ 10 to both sidft to undo .ubtrKIion. Il> JoO<IF >OIu1ion. ",botilllt e 14 for KIn OO9i".1 Vr><e ;;, .ubtr;><fe<f from m,. . dd ; to both >ide. to undo tM "'bIrKIiori. Sol, ... each equadorl. Check your answer. nWlj Ia. " _ 3.2 .. 5.£ lb. _ 6 .. 1" _6 1·1 SoI",'rtg Eqwliom by Adding or SubtrKting 13

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Page 1: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

I

Solving Equations by Adding or Subtracting

..:'II. ~_tI<>l Ouaf/tnt: How <on you u .. ~dd;I;on or 1Ub:'Klion to

.. <01 • • equatio",!

Obl«rl". Sol •• cnHlep equation. in one ... jabl. by u<ir>g addition or ,ublrKtion.

~"Oll"'" equ. tion soIu!;"" of an equllion

'1MhUa1!' Solution. .,. sometime'! written in a ""lIlion ... r. Fe, Example lA, 'M solution .. ' i. (1 4). For example lB, the

",Iution •• !! ;'{H.

Who "HI thlsl Athlete. Can ~ an equation to estimate their maxi mum hean ral"" (See E .. mpl. 4 .)

An "'lua.;o n is. m~,hem"'k~I"Me"""n' 'hot OW<) expressions areequaJ. It ..,hnlon of a n equation is a value of 'he v.riable lila! makes 'he equalionlrue.

To find solution •. isoJnr~ I~ lIa1iabie. It variable is isol.ted when it apP'!ars by i'self on nn~ side of an equation, and not ., all on lhe olher side. lsolale a variable by using i"verse opemlion •. which ·undo· ope .. lions on the variable.

An equation is like a balanced scale. To keep the balarlce. Inv_ Oper.tlons perform the same operation Add x . _ Subtract x . on both skies.

j j t t

Solv ing Equations by Using Addition

Solve eaoh equallon.

x- 10_4

x-IO . 4

-±...!.I!. + 10 x .. 14

Chl!Ck x - 10 ~ 4

14 -10 1' , "

t .. m-t i ," m-t

+.1 +.1 , , t-m

Vr><e ro i. 'UbrrKfe<f from ;(. _ 10 to both sidft to undo t~ .ubtrKIion.

Il> ,1Ie<~ JoO<IF >OIu1ion. ",botilllte 14 for K In t~ OO9i".1 ~u.lion.

Vr><e ;;, .ubtr;><fe<f from m,. . dd ; to both >ide. to undo tM "'bIrKIiori.

~altar} Sol, ... each equadorl. Check your answer. nWlj Ia. " _ 3.2 .. 5.£ lb. _ 6 .. 1" _ 6

1·1 SoI",'rtg Eqwliom by Adding or SubtrKting 13

Page 2: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

(>W>o_,_

Am. W. lk. r (a,,,,,, High S<hool

Solving Equations by Using Subtraction

Sollie eaoh "'Iuallon. (h""k your ans_r.

x+7_9

Chock x +7=9

2+""7T9 9 19.1

0.7.,+0.4 0.7~r+0.4

- 0.4 - 0.4 -- -- -0.3 ~.

Chock 0.7 ~ r + O,~ " I 0.3 + 0.4 0.7 0.7 /

Since 7 ;, ~dod 10 .. SUbUKt lfrom both lidos to undo the .ddition.

To <I>«k joOtI' sohJfion. subJlifvte 1 fot • In tIK; oo9in.l r<lu.oTK>n.

Since 0.4 i, KkJed 10 r, wbl'KtO.4 from bod> ,ido, 10 undo tIK; .ddition.

TO <I>«k joOtI. sohJfion. wbJtifvl. O.J fot. in 1M oogiMJ equ.otion.

~f(Jr} Sol • ..., each "'Iuallon. Cheok your an, .......

t1Q(1fj 2a.d +t_1 2b. _5_ 1'+5 2<:. 6+t _ 14

Remember that SUbtracting i. The .. me U adding the oppu.ite. When solving equations, you will sometimes nnd it ea.ie r 10 add an oppusiTe 10 bolh sides inSTead ofsubl",cting. rOt example, this method may be useful when the equaTion contains negll(ive numbers.

:) Solving Equations by Adding the Opposite Solve -II + b _ 2.

-1I+ b~ 2

~ +11 b _ 10

Zero As a Solution

.k. _ II +;<_33

I <ned to get ronfused wh«Il got a so/ut.-on of 0. But my teacher reminded me thiot 0 is a number jv>t like ~ny oTher number, SO it <;.On be ~ solution of Itn equation. Just <lIe<k JoOIII' .m ...... It"" ..... if it we>rh

I

Page 3: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

I I

FitneH Applicetion

A person's maxi mum hear t rate Is the highest rate. In bea ts per minute, that .he pel'5<ln'. hean . ho. ld ",aell.One me.hod to es. ima te maximum heart rate . tates tha t your age added to your maxlmum hean ra te 1&220. Using th l$ method, write and ""Ive an equation to find the maximum hean raleofa 15·Y""I'0Id.

Age added to maxlmum heart rale Is 220.

" +

15 +, .. 220

- 15 - 15 , .. 205

, '" Write "" <quo'*'" to """"""'. _ rtl.>tmMNp.

Sub>ti"'t~ IS for • . SiIK~ IS i. ~ to T,

w~.rKI IS from bolh skI ... o undo lhe Mldirion.

The maximum heart rate for a IS·year·old ;s205 beat. per minute. Since age added to m""im"", hear( rate i, 220. the answershould be less than 220. So 205 i. a reason.ble answer,

($?[TEa} 4. What If ••• 1 Use the method above to find a ['<'rson'sage if the "OUTJ pe .. on~ max,",um heart rate Is 185 beats ['<'r minute,

The properties of equality allow you to perform inverse operations, 8S In tlte previous examples. These proper(ie!; say that you can ['<'rform the same operation on both sides of an "'luation,

NUMBERS Al"EBRA

Addit"" Property of Equ.oljty You can odd ,he ",me number :0 ,., both .id ... of on equati.,." aOO t .... .. ,

l +l _ l + l <latem"", wil l 'ti ll be true. . +c .~ +< ,. , SubvO(ti.,., ~~ of Equ.li~

You can wbtract the ",me nu~r ,., from both ,id ... of an equation, .. ,

7 _ S _ 7 _ 5 aOO t .... statement will <lill be tr .... . -c .~ - < ,. ,

1. De$cribe how Ihe Addition and Suht""'ti,," Properties ofF.quali.y are li ke a balanced seale,

"U ORGANIZED Copy and complete the graphic organizer_ In each box, wri.e an example of an equa.ion that can be sol>-ed by using the gi''''" propHty, and sol'''' it.

I'rogenieo 01 Equaljty

'·1 5oI .. 'ng Equation. by Addin9 or Su~VKting 15

Page 4: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

SEE E~"'MPLE •

GUIDED PRACTICE

my.hrw.tom

'." .. w,,,H'.'

1. Vocebule ry Wililhe solwio" olan lUI"dli(m such asx - 3 _ 9 be a ,·.nable or. number! Explain.

Sol,.., each equ.'ion. Check you •• nower.

,. 1-5 _ 3 , 17 _ w_ 4 •• k_8 _ _ 7

•• x _ 3.9 .. 12.4 •• 8.4 _1_ 4.6 ,. j - /- i •• /+5 _ _ 25 , 9 _ 1+ 9 ". 42 _ m+36

". 2.8 .. %+0.5 ". b + j_ 2 n. ,,+1.8 _ 3

". _1O+d_7 ". 20 .. _12 + ~ ". _46 +q ~ 5

H. 2.8 __ 0.9 +1 ". - j+c_j ". _~ + P_2

HE EXAMPLE • 20. Geo logy In 1673. the Hope diamond was rruuced from ilS original ",eight by about 45 carats, resulting in a diamond \"reighing about 67 cara". Write and solve an equation to find how many carats the original diamond weigh ...... Show ,hal your answ"r is reasonable.

Iitt j 1 "'Oitflltb ~ * ~ -It-30 ,,~ , .. ~ , .. • o my.hrw.«>m

-I!Jm

PRACTICE AND PROBLEM SOLVING Soh.., each equation. Check you. ans ... er.

". I_ t_ 8 ". 1<_15 __ 8 U x _ 7_10 ". _9_p_2

". ~-p-t ". q-0.5_I.S n 6_1_4.5 ". 4j-r-i

". 6_x _ 3 " 1.75_1: _ 0.75 " 19+,,_19 ". 4 _3.1+1 ... m+W _ 3 ". - 12 .. ,+3 ". ~+ 2300 _ _ 000 ". b+42 _ 300

". 3.5 _ n+4 ". b+t - ! ". x + 5.34 _ 5.39 ~. 2 - d+ t •• - 12+1_ 3 " - 9 - - 4+8 ... _ 1200+} .oo345 « . 90 _ _ 22+"

". 26 _ _ 4+1 ... 1~-- t +W ". -i+h-i ... _5.2+" .. _8

411. lOin e n ... Lui. de_i,"" $500 in'o hi. bonk a <".,,,n" I te now h ... $H12. \\lri'e and solve an equation to find how much was;n hi. aceount hdore the dcposil. Show lhal your answer I. reasonable.

SO. II/ERROR ANALYSISII/ !lelow are lwo possible solutions tox + 12.5 .. 21.6. Which is incorrccl? Explain the elTOr .

• , Il.J· l"

....:...Jl.J. :...ll.1 • . '1

, ·IU"ZI.o ...!.lZ..1 !...lU

." YU

Page 5: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

Wri.e an (>qlL;u ion to 'Cp«$CI" each .elatlonShip. Then solve . he C<juadon.

51. Ten I"n ,h,," "n","ber 1$ equa] 10 12.

52. A nun'i>er decreased by 13 is equal w 7.

Eight more Ihall a ","nber is 16.

A n"n~r minu s 3 I$ ....a.

11 ... sum of5 and a number is 6.

Two Ie .. than a lllunb<>r is-{;.

11,e d ilTerenc~ of a nUJ11~r and 4 h 9.

G_logy 11", sum oftl,..Atlanlic Ocean'sa'wage<kopll' (in feN) a nd its great.,., depth is 43. 126. Use Ihe infonnation in the graph '0 write and 80h" a n equation to find lite a"'laS" depth of tl'" Allantic OcMIt. Show that your an",,,r i, reasonable.

S c hoo l Ilclc'te'$ m.,,,,hing band need. "",ooy to tra",1 to a CO"'I",t;tloll. fund ",eJ11~T$I",,, mi$Cd SSW. l1.,y II""d '" mise a total of $1680. Write and sol,,, an eql~'tio" to find I"",' nll>eh more tltey need. Sh"w Ih" , you. a n~",,::, is reasoll"ble.

60. Econo m ic a \Vh"n ;'0" re<:ei,e a I~ 10 rnnke a ]>1".;,1" ... , ;-ou of I. II rm'S' ,,~,ke a d""" !Myment in cash. 11 ... amOlln , of ~'" loan ], II ... ]",,,,haM co", mlnu, II ... down p"ymenl Rim made ad""" !M}''''''"' ofS 1500 on a used ca r. She re""h"ed a loon of S2WO. Write "nd sol,..:: an (>quation to find d", cnst of 'he Car. Show ,hal you. "li S"'" i~ reasonabl".

G_ ..... try The angles In each pair are complem en ta. )' " .... lte and sol"" an equation 10 find ('a<h value of x. (IU1lI: Thc measures of O<Hnl~cmenLa.y ."gles add to 90'.)

". n.

.'

lILlie! are Oflen used to deseribe how quid")' something Is moving Or changi ng.

a. A "ildflre 'p",ad. at a rn'~ of 1000 acres pcr day. flow ma ny ""re, will d,.. Ii", C","::r III 2 days? Show ~Ull you . ans"", i$ ",asoll"blc.

b. How ",any acres "ill II", fir<' cow, in 5 days? Explain how you found your an,,,,,r.

C. Allo ther "ildfire Sl'read for 7 day. and cowred a total of 700 square nwes. 11",,' can )"0\.1 estimate llle nUInb<.>r of square nwe, d>e n", c",,,red pcr day?

r-l SoMng EqUd'ioru brAnding 01 SubtrKfing 11

Page 6: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

65. SI.linic. The range of a scI of scores il 28. and d .. lowesl !!COre is 47. Wrile a nd wive a n "'I'lalion 10 find die higl .. " !!CO .... (/lim: In a da ta SCI. d .. ra nge 1, 1l1e difference bel ... cen II .. higl .. SI a nd die 10 ... " " ,.,.h,e .. ) Show lllal your an' ..... r is reasonable.

1WI1 66 . Writ. About [1 Describe a real· ,,·o ri.d s;ol.:uio" " UI ' ( .'" be modeled by x + 5 ~ 25. T~II whallhc ,·anable ,,"presenl s in your .in~lI ion. 1l1Cn wI ,-e IIIC equalion and loll ... 1"" Ihe solution meam in Ihe oo n",xl <l your probl .. m.

~ 61. Crit ic. 1 Thinking Wilholli whing. ",U"tlel/ler <I .. wlllllo n of _3 + Z _ 10 wt/[ be greate ' 'hnn 10 n' less ,h. " I O. ~I~ "I".

TEST PREP 68. Whkh situation i, best represent..,;! by x _ 32 .. S?

(!) logan withdrew $32 from her bank a«o,mt After her withdrawal her balance was $8. How much wasortglnally In her a«oont?

<D Daniel I" .. 32 baseball cards. Joseph has 8 fewer baseball cards than Daniel. How many b.»eball cards docs Joseph have?

<t:> Room A (ootains 32 do>Iks. Room S has 8 f..-r do>Iks. How many desks. are In Room S'

~ Janelle rought a bag of 32 a aft sti cks for a project. She used 8 a aft sticks. How many aa ft stldr.sdoos she have left?

69. For ....ttk h equation is a _ 8 a wlution?

«) 15 _ a = 10 <G) 10 + a = 23 (]j) a _ 18 = 26 <D a +8 = 16

70. Short R .. pon • • Julia""" used a gift <llrd to pay for an 518 haircut. The remaining balance on the card _ 522 .

• . Wri te an equation that can be used to determine the original value of the card. b. Solve your equation to find the orIgirai value of the card.

CHALLENCE AND EXTEND Sol"" each eq" ation . Check your an, w«.

72. x - ~-t 74. x-t-t 75. If I' _ 4 .. 2. find d ie ,·a1ue of 5p _ 20. 76. If I + 6 .. 21. find <I .. val'le of_2I.

77 . Ifx+3 =1 5. fi lld<l .. ,.,.luc ofI S+ 6x. n . lf 2+"=- l l. find<l .. ,.,.h .. of6,,.

FOCUS ON MATIEMATICAL PRACTICES R ... oninog CoUll':"':: ,I..., "'Iua1ion$ w .. 3 ~ 65 and 3~ w ~ 65 . 1I0"'~ relllC solll1iOR$ rclmoo?

gI) 80. M . k •• Co RjectU •• Conside r tile equation 8 ~ 8.

~ . How call )"0" ootain ,IIC "'I"a lioll 3 ~ 1 by USiRg 1hc Subtrac tion I'roperty of Equal ily! How call )"0" OO1'3 ill 1/ .. eq'13 lion 3 s 3 by u ,ing 1/ ... ""lditioR I'ro]><' rty of Equality?

b. I, th .. Subtrac tion I'rol'''rty of Equal ily {!\'" nfflled 10 . 01> ... art cq'131ion? Explain .

Page 7: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

Solving Equations by Multiplying or Dividing

8 &u..tlol QIIft_, How con yoo U~ mukiplk.,ion '" di.i,ion te ",Iv. <quati"",?

Ob/tt<tl..-Solve one-,"p oquOlion. in on •• .,i.b'e by U.ir>g multi~iCltlon '" divi'ion.

Who u ses this? Pilot< can make qu ick ca lculation. by solving one-step equation •. {See Exampl. 4.l

Solving an e<Jua!;on lh.l conlains multiplica1ion ard;.i.ion i •• imil.r {osolving an equalion lhat cOnlains addilion or ,ublrac,ion. Use in.-erie operation. to undo the operations on 'he variable.

Remember Iha! an C<Jualion i. like a balanoM &<"ale. To k""p {he balance, what .... ..,' you do cn pne side of{hccqualion. j1)U muSt also de Qn 'he other side.

I,,"I'M Opera tions Multiply by}t. _ Oivi" by Jf.

Solving Equations by Using Multiplication

Solve each "'luallon. Ch<"<k your ans"",r.

_4 .. ~ -, (-5)(- 4) .. (-5l(!s)

"' -, -4 .. ..!.. -,

I' '" -, _ 4 _ 4 ,/

!!!.. .. 1.5 , (3)(~') .. (3}(l.S)

", .. 4.5

S;nce k;' dividN by -5, mul.iply bo.n sIdt< by _5 to undo'M divisiofl.

To cl>ed )'0<1' <olutiofl. "'I><fjlu'~ 10 tot k ., .he origi"'" ~u~6on.

S;"'~ m i, divided by J, multiply both ,j<h. oy J to unao .roe <1M>1On.

To cl>e<k)'O<l' <oiuUon. "'I><'ilut~ 1.5 tot m ., .he origi"'" ~u~6on.

~~ Sol,.., each equation. Che<:k )'Ou. anS".., •.

Ia. t'" 10 1 b. _ 13 " ~ lc. f .. 7 I I

Page 8: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

""",,,,_Tu""

Solving Equations by Using Division

Sol"" eaoh "'IuaUon. Ch""k your ans_rs.

7",_ 56

7; _ s:

13_ - 2w .fl.. _ - 2w - 2 - 2

-6.5 _ w

13 _ 2w

131 - 2( 6.5) 13 13 ./

5in<e K i, mulliplied by 7, divide bolh fflIn by 7 to undo !he multJplk.UO(!,

To cl>«k your sohlfi<><\. wb,tJtu~ B for x in .he orl9i".1 equ.ti""

Sin<e w i, multip/ied by _2, di.,jde both #dn by _2/0 undo the nw/tip/ieotiOll.

TO cl>«k your sohl.ion. wb,,;ru .. _6.~ for w In lhe o<;gl,.., tq<I.tion,

(21;,~ Sol,.., .... oh "'Iuation. Ch""k youcan<wer. 2a. 16~4c l b. O,5y~ - 10

Remember that dividing i~ the . ame as multiplying by the reciprocal. When solving "'Iual>Ons. you "'ill som'times find it easier 10 multiply by a reciprocal Instead nf dividing. This is nfter, ' rue when an "'Iuation romain s fraclions,

Solving Equations That Contain FractioM

Solve eaoh "'Iuation.

%V_35

, " "2-3"

, " 2" " 3

%~ ty

(~)H~) t, ll .. y •

The reclpro<.1 of: is ~ . Since v i, nwltiplied by ~, multiply both side. by i .

The recipro<.' of ~ i':. Since y I. "",/tip/jed

by 1, multiply both side. by~_

(21;,~ Solve each "'Iuauon. Ch""k your an .... ·er.

3a. -i -ib 3b· i .. ~ 3c. ~w _ t02

1·3 SoMI>g Equltion. by Multiplying Of Dj";din9 H

Page 9: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

The equa tion USf'S the pl~",,~ height ~bove the ground in rhou",nci> of feel. So .ubstitute 10 fn< h. not 10.000.

The dMance in mile< from Ihe airporl Ihat a pla ne should begin descendlnll. divided by 3. equals Ihe plane'. helghl above Iheground In Ihou. and. offeel. Ifa plane Is 10.000 feel above .he grou nd. wd.e and .01...., an

10.OOOft

equation 10 Rnd Ihe dl.lance at which Ihe pllol.hould begin descending.

Distance divided by3 equals ~elghlln I~ou ... nd. off 001 .

• - - , , 1"10

(3) 1 .. (3) 10

,- '"

Sub.<I;'ute IQ fo< h. 5i",~ d;, d;'Ii<kd by 3. rrwi';p/y bo'h .;<m by J to undo ,lie dM.iofI.

The pilot should ""&in descending:l) miles from lhe airport.

~~ 4. What If . .. 1 A plane began descend ing45 miles from the n airport, U.., .he eq""lion above to find how high the plane

wa, nying when Ihe dESCent began ,

You ha,'C now used four properties of "",aJily 10 solve equation .. Th".., prorertics ar".ummari • .ed in Ihebo. below.

NUMBERS ALGEBRA

A<kIition Property of fqUlllity You can add the ",me number to bot h ,-, .id .. of an ""Iuation. and the "ate""nt --,

3 +2 _ 3 +2 will "ill be true a +c _ b + < ,- , Subt'M~ Proper1y 01 Eq""'ily

You can ,ubtrKl the "''''' number from ,-, both ,id .. of an equation. --, 7 _ 5 _ 7 _ S .00 tltt ,"''''ment will ,till be tn". a _ c _b _ <

h' M~"'pt' .. Uon _po>r1\I 01 ~q ... '~ You can mult iply both ,id .. of on .-. equat ion by the ..,m. number. 000 Ihe 6(l ) _ 6(J) .-, "olo""nl will still be true , ~ - ~ 18 _ 18

OO.i...", Prope<ty of fq .........

You <.>n div<le both "de. of an .-. .-, ""Iuation by the ... me """,e ro numbe<. t -t «+0) 000 t ltt ,,,,t.,,,,nt wi ll " ill be tn".

,-, f -f

Page 10: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

oct 1 1 m', .. !!',> ~ ~

~-11-18

19-36 1 )1_ J .. . o my.hrw.<Om

-I!Jm

Ameri<on Robo<1 ~ Wdow (1918-1941l) hoId<the~"" WOIId" •• APstman--8 ~ 1 1.1 in. 110 also

hold< WOI1d r"" .. '" "" the lalgtst ,.., aM -_:_---

Solve each equa'ion. Check YOu, answer.

37. %k~5 38. -9~~d ". - ~b~lO .. - ~K~ - 12

... t -- ~q U . - ~ - - ta

45. Flnen ce Afier laxes. Alexandra', lal:e·holme pay is -fo of her salary t>efore taxes. Wri,e and solve an equa.ion '0 nnd Alexandra', salary before ,a;<es fOT 'he pay ~riod .ha. resul.ed in S392 of ,ar.e, home pay.

46. Ee nh Scie nce Your weigh, on 'he Mocn Is about i of your Wilight on F.arlh. Write and sol'"<' an eq"a.ion to show how m"ch a person Wilighs on Eanh if he ","<,ighs 16 ~und. on .he Moon. Howcouid you check .ha. yo"r anSwer is reasonable?

47. II/ERROR MAlYSISlI1 For the equation 1- 15. a student found the "alue of x '0 be 5. fuplain .he error. Wlm i. ,h. cor"",t an'Wilr?

Geometry The perim"'''' of a square Is giv.n. Write and sol,.., an equation '0 find the length of each si de of ,he square.

41. 1' _ 36 in. 49,P_64ln. 50.P _ lOOyd 51. P_16.4cm

Wri'e an ~quation to repTeSent each relatiomhip. Th~n ..,Ive ' he o:<Juation.

Five .imes a number i. 45.

A number muhil'lied by negati,.., 3 is 12.

A number divided by4 i, C<!ual to 10.

The quo.ien. of a number and 3 i. ncgat;"'e 6.

St.tifti". The mean heigh. of'he •• uden •• in Ma".-.class is 60 in. There are 18 .. "den.s in her class. Wri.e and sol,.., an ",ua.;on ,0 find .he .o.al me3$"re of all .. uden.s· heigh.s. (fiinl:The mean is found bydividing .he S"m of all da.a value. by ,he numberofda'a values.)

Flne n"" Usa earned S6.25 per hour al ~er afier.$Chool job. Each w""k she earned s.so. Wrileand solve an equation to sh"",how many houT$ sheworkcd each week.

58. C.hlcel Th inking Will thcsolution of ,\ _ 4 be greatcr than 4 or less than 41 ","plain.

59. Con.ume. Economic. Dion·,long·di'tance I'honc bill was SI3.90. llis Iong·dist"nce calls cost SO.05 per minute. Writc and ..,1,.., an C<!u"tion'o lind ,he n"mbe. of minutes he ,..as charged fo •. Show that your aIlS"'..,. i, reasonable.

60. Nutriti on An 8 OZ CUI' of coffee h3$ al>OO' 164 mgof caffeine. This is 5 ,imes as much caffeine 3$ in a 12 n7 . ..,f, drink. Wri'e and solve an equation '0 find abo", how much caffeine i. in a It o~caffcina'e<1 m drink. Round youT anSWilr'O the nCares. whole numbe •. Show,ha' )"Our an.we. is reasonable.

Use 'he equation Sy _ 4x to nnd y for each value of x.

" " " ..

• ~

-, 0 ,

U 4(_4) __ 16

• • •

8y _ 4x , 81 _ _ 16 • • • • • • • I

Page 11: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

I I

65 . a. TI>e formula for tI>e meanofa dnl.l stl ismean ~ , .. ::::::.. ..... : .... . O'>e

S""Ul>e,. ~1~fI' ,,-en' 1926 wildfl",. in Arizona. Which ,·ah", does ~,il """,her "'pro"",,,, in 11,.. h,muln?

b. TI .. "","n mnn/w, of ""w" b,,">e<i by c"ch ,,;ldfin' "'as 96.21. \~l,kh ,·nl..,.. doe. ~,i" munl><>, "'P"'OOnl in~ ... fo"m~a!

Co Uoo 11 ... K>rmld a and Informalion gi,..,n 10 find how many ""re. "..,re burrK'd by "1Idfi,,," in A,iwn. thai ",nnn ... r. Ro"nd )"0'"' an",..", 10 11K' n"nre" an". SI,.,.,.· IIml YOU' an,,..,,, i, """.onable.

Sol .... each equaUon. O""'k your ""S",OI".

". ': - I ". 4.- _28 u. 1.2h _ 14.4 ". ~.r _121 ". 2w~ 26 " 4b ~ % ". 5y~ II n. ..!!... _ 3

" Biology the the lable for I:Cxertls,,", 74 ""d 75.

74. TI,e UK'a n ",e ighlof a n adull male Tal is 16 Ii",,,. Ihe ",can ,..eighl of a n adl~1 mal e nlOU .... Wnw and , 00 ... e an equation 10 find d", " .. an ,.."ighl of a n adull male mou .... Show thai your a ns,..er Is reasonable.

1'5 . On avc,.. a hm" Slc, al birth " ... igll$ ~ II .. ,..ei:gln of a !l"rbil a l binh.. W,ilc nlld .oh ... nn <'<Iuation 10 find II ... a''''rage we ighl of a gerbil al binh. Show Ihal your ans,.." , is fl'a~"" able .

76. Writ. About It I)(:&<:ribe a real· ,..oM sill.l.11iOll lI"' l ("" be mode led l.>y 3.t z 42. Sol,.., 11K' <'<I""lion and tell "hl1 ~lC lOImion mca ns in 11K' conlexl of YOU' problem.

TEST PREP n. Whkh sltu~tion does NOT represent the equation 1- 10?

a> Leo bought a box of peool .. H. gave half of them to hi. broth .... They each got 10 pern:il •. H<M' man~ peool' """e In the box loo bought?

()) Ka~ _~ diYido!d t- """"'1 from bab~.slttlng Into two bank 3ICCOOrm. Sh'! PI){ flO In '!aW 3«ount. How much did Kasey <!<1m?

<c Gilb<!rt aot a pi<!<le of ribbon Inl0 2·lnch strips. 1Ml<!n h<! was don'!. h<! hold ten 2-lnch strips. How long was the ,ibbon to SUlrt?

CIt> Matti'! had 2 JT\OfE! COs than her sister Leona. If Leona had 10 ct>s, how many COs did Mattie have?

78. WhIch equation b<!Iow srows a conEd fI~t step fOt solving 3>" _ - 12? <D 3x + 3 _ _ 12 + 3 (]I) 3(3.0) _3(_ 12)

<lI)3.o-3 _ _ 12 _ 3 CD ~ _ -~2

1·3 SoMng fQ ""tio'" by M"I~·plyfn9 Of Divfdi'"!l 25

Page 12: Solving Equations by Adding or Subtractinglilliepad.pbworks.com/w/file/fetch/61554085/CA 1.2.pdf · I I FitneH Applicetion A person's maximum heart rate Is the highest rate. In beats

". In a '''9U1ar pentagon, .11 of the angles are equal In """, ... ", The Wrn of the angle """sUO'e. is 540". Whkh of the following equations could be used to tim the !'O"le3SU,e of (NIch aogle?

<!> ~=5

<D 5x .. 540

<0 54Ox = 5

<D> ~. 540

o 80. For IIwtIlch equation Is m ~ 10 a solution?

(1) 5_2m <II) 5m_2 <Jl) ~ = 5

81. Shon R .. pon •• Luisa bOuifll (; cansof cat 1000 th.)t eiKh co.t the same amount She .pent a total of '4.80.

J. Wrlte an equatloo to detem1IM the cst olone can of cat fIx)d. TeU what each part of your equation represents.

b. Solve your equation to flnd the cost cf OM can of cat food. Show each step.

CHALLENCE AND EXTEND Sol"" each C<lu •• ion.01eck your a"ower.

82. (Ji)b .. i 85. (-2:0)k_-26 ,10

Find each indicate<! va' ue.

83. H)X-21 86. H)W:1S~

84. (5t~- -52k 87. (2i)d=41

88. If2p .. 4, find the ,1\1"" olSp + 10. 89, If6r:24,find ~",,,,,lu,,of-51 ,

90. If ll" '" 15, find die ,-aloo ofl2 _ 4.<. 91. If -I '" _I I, nnd d", ,,,It., of 61l

92. To Isolate rln ar .. b, ... ita! .hould yoo divide bod,.id ... by?

93 . To isolaw x in i = h. "h11 """mlion .ho. [d you perfonn on both sides of d>e "'llialion?

li§II 94. Trav. 1 TIle formula d '"' n gi'"'" die di.lllOOO d dlal i. lra",11'd al a ralc r In Unle I. 3. If d _ 400and r _ 25. Wlla1 I, die '·31"" "f H b. If d _ 400 and r _ 50, wlla! I, die '·31"" "f 11

Co Wlwot if ... 1 Ilow did I chang<: ,,1le!l r increased from 25 10 50? d. Wlwot if .. 1 If r is doubll'd while d remain. d .. sa",,,. whal i. d .. cffeCl on t!

FOCUS ON MATHEMATICAL PRACTtcE5 Probl. m Solv i ..... Teodid nol blOWho", manyounc ... of liquid hi. rice cooker cup would hold. lie used d>e cup 10 pul an emire 32·oz contain{'r of brolh imo lhe

coo~cr. filling lhe cup 51 lime$. How nu;h liquid docs dle cup hold?

H!8J 96. Communication Suppose <land bare any l>on",,1O nu"'be .... Soke d",

"'IUalion.!x,", band t;x '"' " f"r .t. Are me oo/mion. d .. san",! Prmide an {'xample

lhal .uppon. )·0'" an.wer.

IiiUI 97. Number S . .... Wriw four "'Iuations 11,n( each ha,,, a solution of 0 and lh.l are 00/,"('(1 by u,ing a differcnlptlll",ny uf eq.mlilY.