6/7 Solving Multi-Step Equations & Inequalities

Solving by Combining Like Terms

100

5h + 2 + 2h

7h + 2

200

3b + b - 8 

4b -8

300

3a + 12 - 6a -2

-3a + 10

400

 -3y + 4 + 5y

2y + 4

500

 3c + 12 - c + 4

2c + 16

Solving by Using the Distributive Property

100

2(x + 5) = 14

x = 2

200

5(d - 2) = 40

d = 10

300

7(4 - t) = -84

t = 16

400

-2(x - 9) = -24

x = 21

500

-13(4 + 2a) = 208

a = -10

Inequalities

100

Solve and graph

 6p - 18 -2p ≤ -2

p ≤ 4

closed circle arrow to the left

200

Solve and graph

-3(4x -5) > 63

x < -4

open circle arrow to the left

300

Solve and graph

 3 - 5(a + 4) > 8

a <-5

open circle arrow to the left

400

Solve and graph

-4 (5x - 2) <  10

x > -1/10 or -0.1

open circle arrow to the right

500

solve and graph

4/5(15x + 45) ≥ -6

x ≥ -3.5

closed circle arrow to the right

Equation Grab Bag

100

4x + 9 = -33

x = -10.5

200

3/4x + 6 = 33

x = 36

300

4(y - 2) + y = -13

y = -1

400

-6(m + 1) + 18 = 24

m = -2

500

7k - 8 + 2(k + 12) = 52

k = 4

Word Problems

100

Write an equation for the problem:

A fifteen passenger van is tented for a family vacation. The van rental is $75 per day, plus a $160 insurance fee. For how many days did the rent the van for if the spent exactly $760 for the van rental?

75x + 160 = 760

200

write an equation and solve

Bella earns $7.50 per hour on the weekends babysitting. How many hours will she need to babysit to earn at least $120?

7.5x ≥ 120

x ≥ 16

300

write an equation and solve

Tyler has 4 boxes of apples. Each box has the same number of apples. After Tyler eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?

4x -3 109

b = 28

400

solve:

Felix joins a local recreation center to play basketball. The recreation center charges a $20 annual fee, plus additional $15 per month for usage of the basketball courts. Felix prepays by writing a check for $185. For how many months did Felix prepay?

11 Months

500

write an inequality and solve

Dylan has $100. He wants to buy a book for $20 and some CDs for $15 each. At most, how many CDs can Dylan buy?

20 + 15x ≤100

x ≤ 5

the answer was 5.8, so he can buy at most 5 CD's