Multi-step Linear Equations Review

Solve for x:

2 1 3x x

1 14x

1 3x

Solve for x:

4 5 1 2 10x x

4 4

1x

6 4 10x

6 6x 6 6

Solve for x:

3 5 14x

15 15

1

3x

3 15 14x

3 1x 3 3

Justine is working on creating a rectangular section of her yard for gardening. She wants the length of the garden to be 2 feet more than twice the width. She has exactly 30 feet worth of fencing material that will make up the perimeter. What will the width of her garden be if she plans to use all 30 feet?

Write an equation for the following:

30 2 2 2 2w w

Let w=width and l=length

Key Information:Shape is a rectanglel=2w+2Perimeter=30 feet

Perimeter Equation for a rectangle

Perimeter=2 length+2 width

w

l=2w+2

P=30 feet

Solve for x:

3 7 2 14x x 14x 14x

5

17x

17 7 2x

17 5x 17 17

77

Solve for x:

12 6 2 4 3x x x

4x12 4 12 4x x

12 124x

All real numbers

Rewrite the equation by clearing fractions:

3 5 75

4 8 2x

8 83 5 7

52

84 8x

6 5 5 28x

Thomas and Dustin are competing to see who can make the most money at a bake sale featuring chocolate chip cookies. Thomas spent $30 on supplies and is selling each cookie for $0.50. Dustin spent $60 on supplies but is selling each cookie for $3.50. At how many cookies will the two have the same profit?

Write an equation for the following:

Profit 0.50 30c

Thomas:Let c=number of cookies sold

Key Information:$30 on supplies (expenses)Each cookie sells for $0.50 (income)

Word Equation

Profit=income-expenses

Profit 3.50 60c

Dustin:Let c=number of cookies sold

Key Information:$60 on supplies (expenses)Each cookie sells for $3.50 (income)Word Equation

Profit=income-expenses

0.50 30 3.50 60c c