Equivalent Expressions
Simplify the expression:
x - 6 - 7 + 6x
7x - 13
Solve:
1 − r = −5
r = 6
Solve:
-2r - 2 < 4
r > -3
Solve:
9 > -2m + 2 - 3
m > -5
Ashlyn needs $150.75 for a Broadway ticket. She already has $62 and she can earn the rest by working 8.5 hours at her job. Write an equation that can be solved to find h, Ashlyn's hourly earnings. YOU DO NOT NEED TO SOLVE.
______ = _______ + _____h
150.75 = 62 + 8.5h
Simplify the expression:
−8(1 − 5x)
-8 + 40x
Solve:
3p − 2 = −29
Solve:
60 > 5 - 5n
n > -11
Solve:
a - 6 < 15 + 8a
a > -3
Natalie budgets $146 for yoga training. She buys a yoga mat for $10.65 and pays $9 per yoga class. Write an inequality to represent the number of classes, c, that Natalie can take and stay within her budget. YOU DO NOT NEED TO SOLVE.
______ ≥ ____c + _____
146 ≥ 9c + 10.65
Simplify the expression:
−2n − (9 − 10n)
8n - 9
Solve:
p/4 + 8 = 7
p = -4
Solve:
-2 + x/2 > 6
x > 16
Solve:
6 - 4(6n + 7) > 122
n < -6
Everly ordered boxed lunches for a student advisory committee meeting. Each lunch costs $6.75. The total cost of the lunches is $207.75, including a $12 delivery fee. Write and solve an equation to find x, the number of boxed lunches Everly ordered.
Everly ordered 29 lunches.
207.75 = 12 + 6.75x
Simplify the expression:
−10(1 − 9x) + 6(x − 10)
-70 + 96x
Solve:
−14r − 19 = 303
r = -23
Solve:
2(4x + 1) < 138
x < 17
Solve:
28 - 7x < -4(-7x - 7)
x > 0
Riley has $10.75 to buy school supplies. She spends $3.96 at one store for a package of glue sticks, but she still needs to buy 3 pens and a notebook. At the next store, she finds pens for $1.39 each.
What is the most she can spend on a notebook if she buys the 3 pens?
$2.62
Simplify the expression:
−7(n + 3) − 8(1 + 8n)
−71n − 29
Solve:
(-12 + x)/11 = -3
x = -21
Solve:
-1 > (12 + x)/4
x < -16
Solve:
-5n + 6 > -7(5n - 6) - 6n
n > 1
A community center is offering a painting class. The instructor is paid $150 plus $48 per person enrolled. How many people need to enroll for the instructor to earn at least $600? Write and solve an inequality to represent this situation.
150 + 48p ≥ 600
p ≥ 9.375
The instructor needs 10 or more people to enroll to earn at least $600.