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

Infinite Solutions, Consistent Solutions, or Inconsistent/No solutions

100

2x +4 = -2(1/2 - x)

No solution

200

6y+(16-2y)=4(4+y)

Identity/Infinite Solutions

300

4x+5=2x-7

Consistent; x=-6

400

2x + 5 = -4(-5/4-1/2x)

Identity/Infinite Solutions

500

1/3x+5=1/6(2x-5)

No solution/Inconsistent

Equation Grab Bag

100

3(6-4x)-27x=10x-31

x = 1

200

3.2a-5=5-1.8a

a = 2

300

4(y - 2) + y = -13

y = -1

400

3x-0.4(5-2x)=5.6

x = 2

500

0.4(x+0.7)=0.6x-4.2

x= 22.4

Word Problems

100

WRITE AN EQUATION & SOLVE: Elmo bought some pencils at 50 cents each. He had $3 left after the purchase. If he wanted to buy the same number of note pads at 80 cents each, he would be short $1.50. Write a linear equation for the number of pencils he purchased. Then solve it.

0.5x+3=0.8x-1.5

x=15

Elmo bought 15 pencils

200

Mr. Cushman bought 7 Stranger Things t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many t-shirts did Mr. Cushman buy? Write an equation and solve.

n - # of t-shirts 7n = 90.93 n = 12.99 Each t-shirt cost $12.99

300

Mal is x years old today. Her friend Carlos is 4 years older. After seven years, their total combined age will be 24 years. Write a linear equation for their total combined age after 7 years. Find Jane's age today.

2x+18=24

Jane is 3 years old today

400

In a grocery store, each pound of grapes costs one a quarter times the price of each pound of potatoes. Mrs. Burns bought 4 pounds of grapes and 5 pounds of potatoes. Mrs. Hall bought 10 pounds of potatoes. They paid the same amount. Write a linear equation to find the cost of each pound of potatoes in p dollars.

4 * 5/4p + 5p=10p

500

When you count by ones fron many integer, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?

n + n + 1 + n + 2 = 48 n = 15 The integers are 15, 16, and 17.