1. Solving Two- Step Equations
Lesson 4-4

2. Rules to Remember
When solving an equation, the goal is to get the variable by itself.
3x + 2 = 9
Addition and Subtraction are opposites
Multiplication and Division are opposites

3. Don’t Forget
The equation is like a balance scale. Whatever you do to one side of the equation must be done to the other side of the equation. +5 +5

4. How to solve two-step equations
“Undo” the operations in the reverse order of the order of operations.
Work back-words SADMEP
Add/Subtract FIRST
Multiply/Divide SECOND

5. Let’s Try One… 3x + 2 = 23 - 2 -2 21 3x = 21 3 3 x = 7 21
3x = 21
x = 7
The problem contains addition and multiplication. Which one do we undo 1st?

6. Another Example -2y – 7 = 3 +7 +7 10 -2y = 10 -2 -2 y = -5 10
-2y = 10
y = -5
The problem contains subtraction and multiplication. Which one do we undo 1st?

7. Last Example -3c + 9 = 3 -9 -9 -6 -3c = -6 -3 -3 c = 2 -6
-3c = -6
c = 2
The problem contains addition and multiplication. Which one do we undo 1st?

8. Solving Two-Step Equations
Solve each equation.
18 + 3x = 30
18 + 3x = 30
– –18
Subtract 18 from both sides to
undo the addition.
3x = 12 3x 3
= 12
Divide both sides by 3 to undo
the multiplication.
x = 4

9. Now it’s your turn 5x + 4 = 19 2t + 7 = -1 6m + 1 = -23 -4w – 4 = 8

10. Solving Two-Step Equations
Solve. Check the answer. x 3
– 2 = 1 x 3
– 2 = 1
Add 2 to both sides to undo
the subtraction. x 3
= 3
3 · = 3 · 3 x 3
Multiply both sides by 3.
x = 9

11. Check It Out: Example 1A
Solve each equation.
12 + 3x = 27
12 + 3x = 27
– –12
Subtract 12 from both sides to
undo the addition.
3x = 15 3x 3
= 15
Divide both sides by 3 to undo
the multiplication.
x = 5

12. Check It Out: Example 1B
Solve. Check the answer. x 2
– 1 = 2 x 2
– 1 = 2
Add 1 to both sides to undo
the subtraction. x 2
= 3
2 · = 2 · 3 x 2
Multiply both sides by 2.
x = 6