Warm-Up Translate each phrase into a variable expression. Let n stand for the number. 1.) five times a number 2.) one third of a number 3.) eight minus twice a number 4.) six less than a number Simplify.

1.)3 + 2x - 2x 2.)2 4t +6 - 4t

2 23.)55 - 2w + 2w 4.) s +5 - s

5 5

5.)8 +5 x -1 - x 6.)- 333u+ 22 +333u

Did you get these answers? Translate each phrase into a variable expression. Let n stand for the number.

1.) five times a number 5n

2.) one third of a number ( 1/3 )n

3.) eight minus twice a number 8 – 2n

4.) six less than a number n - 6

Simplify.

1.) 3 + 2x - 2x = 3 2.) 2 4t + 6 - 4t = 4t +12

2 23.) 55 - 2w + 2w = 55 4.) s + 5 - s = 5

5 5

5.) 8 + 5 x -1 - x = 4x + 3 6.) - 333u + 22 + 333u = 22

Homework Questions?

Section 3-4

Using Equations to Solve Problems

Objective

I want to be able to use the five-step plan to solve word problems.

Plan for Solving a Word Problem

Step 1 – Read the problem carefully. Decide what unknown numbers are asked for and what facts are known. Making a sketch may help.

Step 2 – Choose a variable and use it with the given facts to represent the unknowns described in the problem.

Plan for Solving a Word Problem

Step 3 – Reread the problem and write an equation that represents relationships among the numbers in the problem.

Step 4 – Solve the equation and find the unknowns asked for.

Step 5 – Check your results with the words of the problem. Give the answer.

Example 1 Sarah already has 45 stamps in her

collection, and she gets 7 new stamps each month. How long will it take before she has 129 stamps in her collection?

Step 1: The problem asks for the time it will take to get 129 stamps.

Example 1 continued

Step 2:

Let m = the number of months it will take.

Step 3:

Future stamps = current stamps plus 7 more each month

129 = 45 + 7m

Example 1 Continued

Step 4:

129 = 45 + 7m

-45 -45

84 = 7m

12 = m

It will take Sarah 12 months to have 129 stamps in her collection.

Example 1 Continued

Step 5:

45 + 7 ( 12 ) = 129

45 + 84 = 129

129 = 129

Example 2

The length of a rectangle is 3 inches more than the width. Find the length and width if the perimeter of the rectangle is 98 inches.

Step 1: the problems asks for the length and width of the rectangle.

Example 2 Continued

Step 2: Let w = the width of the rectangle. Then w + 3 = the length of the rectangle.

Step 3: Use the formula P = 2l + 2w

Step 4:

98 = 2(w + 3) + 2w

98 = 2w + 6 + 2w

98 = 4w + 6

92 = 4 w

23 = w

Example 2 Continued

Step 5:

The length of the rectangle is 26 in. and the width is 23 in.

2 ( 26) + 2 ( 23 ) = 52 + 46 = 98

Section 3-5

Equations with the Variable on Both Sides

Objective

I want to be able to solve equations with the variable on both sides.

Example 1

Solve. 20+7x = 9x

Example 2

Solve. 4t = 50-6t

Example 3

Solve. 3 8x = 4 - x

5 5

Example 4

Solve. 4 r - 9 +2 =12r +14

Example 5

Solve. 3 x +2 - x = 2 x +1

Example 6

Solve. 2 3y +5 +9 = 6 y +3 +1

Try These! Solve each problem using the five-step plan. 1.) Six less than five times a number is 74.

Find the number. 2.) Eight less than one half a number is -44.

Find the number. 3.) Tom has read 143 pages of the 251 pages

in a book. If he reads 12 pages a day, how long will it take him to finish the book?

4.) The longest side of a triangle is 3 more

than twice the shortest side and the remaining side is 2.4 cm. Find the lengths if the perimeter is 12 cm.

Try These! Solve each problem using the five-step plan. 1.) Six less than five times a number is 74. Find

the number. 16 2.) Eight less than one half a number is -44. Find

the number. - 72 3.) Tom has read 143 pages of the 251 pages in a

book. If he reads 12 pages a day, how long will it take him to finish the book? 9 days

4.) The longest side of a triangle is 3 more than

twice the shortest side and the remaining side is 2.4 cm. Find the lengths if the perimeter is 12 cm. 2.4, 2.2, 7.4 cm

Algebra Activity

Solving Equations (Variables on Both Sides of the Equal Sign)

And These!

1.) 9x = 2x + 21 4. ) 3 k - 8 = k + 4

x +102.) 4t = 60 - 8t 5 .) = 2x

3

2x - 73.) 2w = 42 +9w 6.) = 3x

2

7.) Find a number whose product wit h 10 is the same

as its sum with 45.

And These!

1.) 9x = 2x + 21 4. ) 3 k - 8 = k + 4

x = 3 k = 14

x +102.) 4t = 60 - 8t 5 .) = 2x

3

t = 5 x = 2

2x - 73.) 2w = 42 +9w 6.) = 3x

2

7 w = - 6 x = -

4

7.) Find a number whose product with 10 is the same

as its sum with 45. 5

Clear your calculators!

Take out your agendas!

Copy down DUE DATES!

Homework:

Sections

3.4, 3.5

Journal Entry

TOPIC: Solving Equations

Answer the following question: Write the examples that had the empty set and identity as the solution. Explain what is meant by an empty set/null set and an identity. (Hint: look on pg. 117)