Solutions to an Equations & Inequalities

Solving by Combining Like Terms

100

5h + 2 + 2h = 23

h = 3

200

3b + b - 8 = 4

b = 3

300

3a + 12 - 6a = -9

a = 7

400

-6 = -3y + 4 + 5y

y = -5

500

78 = 3c + 12 - c + 4

c = 31

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. 6p - 18 -2p ≤ -2

p ≤ 4

200

Solve. 2(6x - 5) < 14

x < 2

300

Solve. 3 - 5(a + 4) ≥ -a + 7

a ≤ -4

400

Solve. -4 (5x - 2) ≥ 4x + 5

1/8 or .125

500

4/5(15x + 45) ≥ -6x

x ≥ -2

Numbers of Equations

100

How many solutions?

4g - 9 =2g- 33

One Solution

g=-12

200

How many solutions?

x + 3x = -2(x+x)

No solution

4x=-4x

300

4(y - 2) + y = -13

y = -1

400

How many solutions?

-6(m + 1) + 18 = -6m-12+24

Infinite Solutions

-6m+12=-6m+12

12=12

500

How many solutions?

6.6k - 8 + 2(1.2k + 8.5) =9k- 11.2

No Solutions

9=11.2

Word Problems

100

WRITE AN EQUATION & SOLVE: Julie is 3 years older than her sister. Julie's age is 11 years old. How old is her sister?

n - Julie's sister's age n + 3 = 11 n = 8 Julie's sister is 8 years old.

200

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

x ≥ 16

300

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?

b = 28

400

Mr. Bucci goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. His total cost was $34.76. What was the cost for a bag of raisins?

r - cost of a bag of raisins 17r + 2.97 = 34.76 r = 1.87 Each bag of raisins cost $1.87

500

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?

C = 5 (Interpret the quotient)