1. 3.1 Solving Two-Step Equations 1 3x + 7 = –5 3x + 7 = –5 – 7 – 7
LESSON
Solving Two-Step Equations
EXAMPLE 1
Using Subtraction and Division to Solve
Solve 3x + 7 = –5. Check your solution.
SOLUTION
3x + 7 = –5
Write original equation.
3x = –5
– – 7
Subtract 7 from each side.
3x = –12
Simplify.
3x = –12 =
Divide each side by 3.
x = –4
Simplify.
ANSWER
The solution is –4.

2. 3.1 Solving Two-Step Equations 1 3x + 7 = –5 3(–4) + 7 = –5 –5 = –5
LESSON
Solving Two-Step Equations
EXAMPLE 1
Using Subtraction and Division to Solve
Solve 3x + 7 = –5. Check your solution.
ANSWER
The solution is –4.
CHECK
3x + 7 = –5
Write original equation.
3(–4) + 7 = –5 ?
Substitute –4 for x.
–5 = –5
Solution checks.

3. 3.1 Solving Two-Step Equations 2 – 3 = 1 – 3 = 1 + 3 + 3 = 4 ( ) = (4)
LESSON
Solving Two-Step Equations
EXAMPLE 2
Using Addition and Multiplication to Solve
Solve – 3 = 1. Check your solution. x 2
SOLUTION
– 3 = 1 x 2
Write original equation.
– = 1 x 2
Add 3 to each side.
= 4 x 2
Simplify.
( ) = (4) x 2
Multiply each side by 2.
x = 8
Simplify.
ANSWER
The solution is 8.

4. 3.1 Solving Two-Step Equations 2 – 3 = 1 – 3 = 1 1 = 1
LESSON
Solving Two-Step Equations
EXAMPLE 2
Using Addition and Multiplication to Solve
Solve – 3 = 1. Check your solution. x 2
ANSWER
The solution is 8.
CHECK
– 3 = 1 x 2
Write original equation.
– 3 = 1 8 2 ?
Substitute 8 for x.
1 = 1
Solution checks.

5. 3.1 Solving Two-Step Equations 3 7 – 4y = 19 7 – 4y = 19 – 7 – 7
LESSON
Solving Two-Step Equations
EXAMPLE 3
Solving an Equation with Negative Coefficients
Solve 7 – 4y = 19. Check your solution.
SOLUTION
7 – 4y = 19
Write original equation.
7 – 4y = 19
– – 7
Subtract 7 from each side.
–4y = 12
Simplify.
–4y = 12
–4 –4 =
Divide each side by –4.
x = –3
Simplify.
ANSWER
The solution is –3.

6. 3.1 Solving Two-Step Equations 3 7 – 4y = 19 7 – 4(–3) = 19 19 = 19
LESSON
Solving Two-Step Equations
EXAMPLE 3
Solving an Equation with Negative Coefficients
Solve 7 – 4y = 19. Check your solution.
ANSWER
The solution is –3.
CHECK
7 – 4y = 19
Write original equation.
7 – 4(–3) = 19 ?
Substitute –3 for y.
19 = 19
Solution checks.

7. 3.1 Solving Two-Step Equations
LESSON
Solving Two-Step Equations
Drum Set You are buying a drum set that costs $495. The music store lets you make a down payment. You can pay the remaining cost in three equal monthly payments with no interest charged. You make a down payment of $150. How much is each monthly payment? You will see how to answer this question by writing and solving a two-step equation.
You can solve a two-step equation by using two inverse operations.

8. 3.1 Solving Two-Step Equations 4 495 = 150 + 3p
LESSON
Solving Two-Step Equations
EXAMPLE 4
Writing and Solving a Two-Step Equation
Find the monthly payment for the drum set described on Slide 1.
SOLUTION
Let p represent the monthly payment. Write a verbal model.
Total cost
of drum set =
Amount of
down payment +
Monthly
payment
Number
of months •
495 = p
Substitute.

9. 3.1 Solving Two-Step Equations 4 495 = 150 + 3p 495 = 150 + 3p
LESSON
Solving Two-Step Equations
EXAMPLE 4
Writing and Solving a Two-Step Equation
Find the monthly payment for the drum set described on Slide 1.
SOLUTION
Substitute.
495 = p
= p
– – 150
Subtract 150 from each side.
345 = 3p
Simplify. p =
Divide each side by 3.
115 = p
Simplify.
ANSWER
The monthly payment is $115.