7th Grade Math

Solve Two-Step Equations

Solve 3x + 2 = 23. Check your solution.

3 x + 2 = 23 Write the equation.

• ____ 2 = - 2 Undo the addition first by subtracting 2 from each side.
  3 x = 21
  ^3 x
  3
  = ^21
  3
  Division Property of Equality
  x = 7 Simplify.
  Check 3 x + 2 = 23 Write the original equation.
  3 (7) + 2  23 Replace x with 7.
  23 = 23 ✓ The sentence is true.
  The solution is 7.

Solve - 2 y - 7 = 3. Check your solution.

• 2 y - 7 = 3 Write the equation.

• __ 7 = + 7 Undo the subtraction first by adding 7 to each side.

• 2 y = 10
  
  
  • 2 y
    _
  
  
  
  


• 2
  = _^10


• 2
  Division Property of Equality
  y = - 5 Simplify.
  The solution is -5. Check the solution.

Solve 4 + _^1

5

r = -1. Check your solution.

4 + _^1

5

r = - 1 Write the equation.

• 4 ___= - 4 Undo the addition first by subtracting 4 from each side.
  _^1
  5
  r = - 5

5 · _^1

5

r = 5 · (-5) Multiplication Property of Equality

r = - 25 Simplify.

The solution is -25. Check the solution.

d. 4 x + 5 = 13 e. - 5 s + 8 = - 2 f. - 2 + _^2

3

w = 10

Solving Two-Step Equations

Step 1 Undo the addition or subtraction first.

Step 2 Then undo the multiplication or division.

Order of Operations Order of Operations

Multiplication comes

before addition in the

order of operations. To

undo these operations,

reverse the order. So,

undo the addition first by

subtracting. Then, undo

the multiplication by

dividing.

Equations Equations Remember,

solutions of the new

equation are also solutions

of the original equation.

Lesson 3B Multi-Step Equations 231

228_239_C04L3_895130.indd 231 12/31/09 3:59 PM