Solving Multi-Step Equations

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

Variables on Both Sides

100

3x+2=5x

x=1

200

x-5=2x

x=-5

300

6r+7=13+7r

r=-6

400

5+2x=2x+6

No Solution

500

-8n+4(1+5n)=-6n-14

n=-1

Grab Bag

100

y/4 =-6

y=-24

200

x+4=-10

x=-14

300

4x + 9 = 33

x = 6

400

6 - 4y=-24

y=7.5

500

-6(m + 1) + 18 = 24

m = -2

600

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

k = 4

Word Problems

100

Translate:

three times a number and 7 is equal to negative 9

3n+7=-9

200

Translate:

the difference of twice a number and eight is 17

2n-8=17

300

Translate:

five less than the quotient of a number and 3 is equal to 20

n/3 -5=20

400

Mr. Cushman bought 7 Hannah Montana t-shirts and a program that cost $6.23 for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Cushman buy?

n=# of t-shirts

Equation : 7n+6.23=90.93

n=12.1

Each shirt cost $12.10

500

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

600

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?

a - # of apples in each box 4a - 3 = 109 a = 28 There were 28 apples in each box.