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You can solve a two-step equation by using two inverse operations.

3.1. Solving Two-Step Equations. LESSON.

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You can solve a two-step equation by using two inverse operations.

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  1. 3.1 Solving Two-Step Equations LESSON 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.

  2. 3.1 Solving Two-Step Equations LESSON 1 EXAMPLE = 3 3 Using Subtraction and Division to Solve Solve 3x + 7 = –5. Check your solution. SOLUTION 3x + 7= –5 Write original equation. 3x + 7 = –5 – 7 – 7 Subtract 7 from each side. 3x = –12 Simplify. 3x = –12 Divide each side by 3. x= –4 Simplify. ANSWER The solution is –4.

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

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

  5. 3.1 Solving Two-Step Equations LESSON 2 EXAMPLE x x 8 Solve – 3 = 1. Check your solution. 2 2 2 ANSWER The solution is 8. – 3= 1 – 3= 1 CHECK ? Using Addition and Multiplication to Solve Write original equation. Substitute 8 for x. 1= 1 Solution checks.

  6. 3.1 Solving Two-Step Equations LESSON 3 EXAMPLE = –4 –4 Solving an Equation with Negative Coefficients Solve 7 – 4y = 19. Check your solution. SOLUTION 7 – 4y= 19 Write original equation. 7 – 4y= 19 – 7 – 7 Subtract 7 from each side. –4y = 12 Simplify. –4y = 12 Divide each side by –4. x= –3 Simplify. ANSWER The solution is –3.

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

  8. 3.1 Solving Two-Step Equations LESSON 4 EXAMPLE Total cost of drum set Amount of down payment Number of months Monthly payment + • = 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. 495 = 150 + 3p Substitute.

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

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