7th Grade Math

Multi-Step Equations

PART A BCD E

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

SPI 0706.3.6.

236 Equations and Inequalities

Main Idea

Use the properties of

equality to simplify

and solve equations

with variables on each

side.

Solve Equations with

Variables on Each Side

FOOD Julian takes two orders

at the fast food restaurant

where he works. One order

is for two hamburgers and

three orders of fries. The

other order is for three

hamburgers and one order

of fries. The two orders cost

the same.

1. If an order of fries costs $2, write expressions for each order.


2. How could you show the expressions are equal?

You can use the properties of equality to solve equations with

variables on each side. The new equation is equivalent to the

original equation.

Writing Equivalent Equations

Express 2x + 6 = 3 x + 2 as an equivalent equation.

Method 2 Subtract a Number

2 x + 6 = 3 x + 2 Write the equation.

• 2 = - 2 Subtract 2 from each side of the equation.
  2 x + 4 = 3 x Simplify.

Method 1 Subtract a Variable

2 x + 6 = 3 x + 2 Write the equation.

• 2 x = - 2 x Subtract 2x from each side of the equation.
  6 = x + 2 Simplify.

So, 2x + 6 = 3 x + 2 is equivalent to 6 = x + 2 and 2x + 4 = 3 x.

Express each equation as another equivalent equation using

properties of equality. Justify your answer.

a. 2 x + 4 = x + 6 b. 3 x - 4 = x - 6

atthe

orders

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