Objective- To recognize symbols, variables, and types of sentences used in algebra.
Equalities Inequalities
= Equals- is the same as
Congruent- same size and shape
Similar- same shape
< Is less than
> Is greater than
Is less than or equal to
Approx. equal to
= Not equal to
~
Expressions vs. Equations
Numerical
Variable
Expressions Equations Inequalities
2 + 35(8) - 4
x + 78 - 3y
2 + 3 = 54 + 2(3) = 10
x - 4 = 1311= 3 + 2m
9 - 5 > 3
6y - 4 < 8
Sentences
Open sentences
Open sentences have solutions and can be solved.
Identify each as an expression, sentence, open sentence, equation, or inequality.
1) 3x + 5 = 11
2) 7 < 2(5) + 3
3) 5x - 2
4) 6m + 2 > 3
Sentence, open sentence, equation
Sentence, inequality
Expression
Sentence, open sentence, inequality
Open sentences have solutions and can be solved.
Variable Equations Variable Inequalities
4 + m = 7 5 + y < 91- 4 - 4
m = 3
- 5 - 5
y < 86
One Solution InfiniteSolutions
Give three solutions to each sentence below.
1) x > 10
2) x + 3 7
3) 5 - x < 0
4) 2 1 3x
Samples: 11, 15, 34
Samples: 4, -8, 0
Samples: 6, 7, 10
Samples: 3, 4, 7
Objective - To translate English words, phrases, and sentences into mathematical symbols, expressions, and equations respectively.
+ _ plusadd
increased bysum
more than
minussubtract
decreased bydiminished by
less thansubtracted from
differenceless
total
product…of...
twice ( 2)
timesmultiply
dividequotient
Tricky Ones!
5 plus x 5 + x
add 5 and x 5 + x
the sum of 5 and x 5 + x
5 increased by x 5 + x
5 more than x x + 5
5 is more than x 5 > x
Tricky Ones!
5 minus x 5 - x
5 less x 5 - x
the difference of 5 and x 5 - x
5 decreased by x 5 - x
5 is less than x 5 < x
5 less than x x - 5
5 subtracted from x x - 5
Translate each phrase into a mathematical expression.
1) 5 subtract x
2) the product of 10 and y
3) 20 decreased by a number t
4) 6 added to the product of 11 and m
5) the quotient of y and 9
6) 8 less than 7 times k
5 - x
10y
20 - t
11m + 6
y 9
7k - 8
Translate each phrase into a mathematical expression.
1) six less than twice a number x
2) five times the sum of y and 4
3) twice the difference of m and 3
4) the quotient of 7 and a number x less 2
5) the difference of 6 and k divided by 9
6) 4 times the sum of 12 and y
2x - 6
5(y + 4)
2(m - 3)
(6 - k) 9
7 x - 2
4(12 + y)
Translate each sentence into a mathematical equation or inequality.
1) Eight less than twice the sum of four and y is the same as 19.
2) Six more than x is more than twice the difference of x and 7.
3) The quotient of m and 3 is six less than theproduct of 10 and m.
4) Five less than x is less than five less x.
2(4 + y) - 8 = 19
x + 6 > 2(x - 7)
x - 5 < 5 - x
m 3 = 10m - 6