1. Solving Addition and Subtraction Equations

2. One way to solve an equation is to use inverse operations. Inverse Operations is an operation that undoes another operation. x + 7 = 10 Solve the equation – – 7 1. Write original equation. 2. Subtract 7 from each side. 3. Simplify. x + 7 = 10 – x –17 = STEPS Solving an Addition Equation

3. EXAMPLE 1 Solving an Addition Equation x + 7 = 10 Solve the equation – – 7 Write original equation. Subtract 7 from each side. Simplify. x + 7 = 10 – Check x + 7 = –10 – 10 = –10 Write original equation. Solution checks. x –17 = 17 + 7 = –10 – Substitute 17 for x. – ?

4. Solve the equation. Check your solution. GUIDED PRACTICE t + 8 = 15 1. 7 ANSWER n + 10 = 4 2. –6 ANSWER 8 + x = –4 3. –12 ANSWER

5. EXAMPLE 2 Solving a Subtraction Equation Solve the equation 9 = y 12– – – – 9 +12 = y 12 + 12 – – 3 = y Write original equation. Add 12 to each side. Simplify.

6. 2 = 1.3 + a + 4 EXAMPLE 3 Combining Like Terms Solve the equation Write original equation. Combine like terms. Subtract 5.3 from each side. Simplify. 2 = 1.3 + a + 4 2 = 5.3 + a 2 5.3 = 5.3 5.3 + a – – – 3.3 = a Check 2 = 1.3 + a + 4 2 = 1.3 + (–3.3) + 4 ? 2 = 2 Write original equation. Substitute – 3.3 for a. Solution checks.

7. Solve the equation. Check your solution. GUIDED PRACTICE 4. 8 = m 6 – 14 ANSWER 5. r 10 = 14– 24 ANSWER 6. 5 = 4 + c – 2 3 ANSWER 7. 2y – 1 – y = – 3 –2 ANSWER 8. 3.4 + s – 1.3 = 6.8 4.7 ANSWER

8. EXAMPLE 4 Writing and Solving an Equation Space Exploration The Apollo 11 mission lasted about 195.5 hours. The flight from Earth to the moon lasted about 103 hours, and the flight from the moon back to Earth lasted about 71 hours. About how many hours did the Apollo 11 astronauts spend on the moon?

9. EXAMPLE 4 Writing and Solving an Equation 195.5 = 103 + t + 71 195.5 = 174 + t 195.5 – 174 = 174 – 174 + t 21.5 = t Write equation. Combine like terms. Subtract 174 from each side. Simplify. The Apollo 11 astronauts spent about 21.5 hours on the moon. ANSWER SOLUTION Write a verbal model. Let t represent the number of hours the astronauts spent on the moon.

10. GUIDED PRACTICE for Example 4 You spent a total of $ 50 for streamers, balloons, and flowers. You spent $ 12.50 on streamers and $ 15 on balloons. Write and solve an equation to find how much you spent on flowers. Decorations f + 12.50 + 15 = 50 f + 27.50 = 50 f + 27.50 – 27.50 = 50 – 27.50 f = $22.50 ANSWER