Rational Numbers & Equations Lesson 4.3 Rational Numbers & Equations Solving Two-Step Equations

Warm-Up Solve each equation. Show your work and check the solution. –6x = – 42 6 = 8 + y p = –12 h = 24.7 x = 7 y = –2

Solving Two-Step Equations Lesson 4.3 Solving Two-Step Equations Solve two-step equations.

Example 1 Solve the equation for the variable. Check the solution. Write the equation. Subtract 2 from both sides of the equation. Multiply each side by 7.  Check the solution. x = –56 –2 –2

Example 2 Solve the equation for x. Check the solution. 12 – 5x = 2 Subtract 12 from both sides. Divide each side by (–5).  Check the solution x = 2 12 – 5x = 2 –12 –12 –5x = –10 x = 2 12 – 5(2) = 2 12 – 10 = 2 2 = 2 –5 –5

Example 3 Deborah opened an ice cream stand at the local pool last summer. She spent $148 on a freezer to start her business. She earned a profit of $0.75 for each ice cream cone she sold. She earned a total of $452 during the summer. How many ice cream cones did Deborah sell? Write the equation: Add 148 to both sides. Divide each side by 0.75.  Check the solution. Deborah sold 800 ice cream cones last summer. 0.75x – 148 = 452 + 148 +148 0.75x = 600 0.75 0.75 x = 800 0.75(800) – 148 452 600 – 148 452 452 = 452

Communication Prompt What do you think are the most common errors students make when solving a two-step equation? Why do you think this is?

Exit Problems Solve each equation. Show your work and check the solution. 1. 2x – 8 = 12 2. –5 = + 1 3 0.6m + 4 = 7 4. –8 + = 2 x = 10 y = –18 m = 5 b = 60