7th Grade Math

Multi-Step Equations

PART A B CD

Multi-Part

Lesson 3

Get ConnectED

GLE 0706.3.8

Use a variety of strategies

to efficiently solve linear

equations and inequalities.

SPI 0706.3.8 Solve

contextual problems

involving two-step linear

equations. Also addresses

GLE 0706.3.7, SPI 0706.3.6,

SPI 0706.3.7.

Main Idea

Solve two-step

equations.

Vocabulary

two-step equation

Solve Two-Step Equations

A florist charges $2 for each

balloon in an arrangement and

a $3 delivery fee. You have $9 to

spend. The model illustrates the

equation 2x + 3 = 9, where x

represents the number of balloons.

To solve 2x + 3 = 9, remove three

1-tiles from each side of the mat.

Then divide the remaining tiles

into two equal groups. The

solution of 2x + 3 = 9 is 3.

Solve each equation by using

algebra tiles or a drawing.

1. 2 x + 1 = 5


2. 3 x + 2 = 8


3. 2 = 5 x + 2

A two-step equation has two different operations. To solve a two-step

equation, undo the operations in reverse order of the order of operations.

Solve a Two-Step Equation

Solve 2x + 3 = 9. Check your solution.

2 x + 3 = 9 Write the equation.

• ____ 3 = - 3 Undo the addition first by subtracting 3 from each side.
  2 x = 6
  ^2 x
  2
  = _^6
  2
  Next, undo the multiplication by dividing each side by 2.
  x = 3 Simplify.
  Check Since 2(3) + 3 = 9, the solution is 3. 

Solve each equation. Check your solution.

a. 2 x + 4 = 10 b. 3 x + 5 = 14 c. 5 = 2 + 3 x

230 Equations and Inequalities

=

Y

Y

1 1

1

1

1

1

1

1

1

1 1 1

2 x + 39 =

=

Y

Y

1 1

1

1

1

1

1

1 1

1

1

1

2 x + 3 - 3 = 9 - 3

Y =

Y 1 1 1

Y 1 1 1

x = 3

V

t

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