1. 2.2 Solve One-Step Equations You will solve one-step equations using algebra. Essential Question: How do you solve one- step equations using subtraction, addition, division, and multiplication?

2. Warm-Up Exercises Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of equality: Subtract 7 from each side. x = –3x = –3 Simplify. ANSWER The solution is –3.

3. Warm-Up Exercises Solve an equation using subtraction EXAMPLE 1 CHECK Substitute –3 for x in the original equation. x + 7 = 4x + 7 = 4 Write original equation. –3 + 7 = 4 ? Substitute – 3 for x. 4 = 44 = 4 Simplify. Solution checks.

4. Warm-Up Exercises Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x – 12 = 3 Write original equation. x – 12 = 3 Add 12 to each side. + 12 x = 15 Simplify. x = 15 x – 12 + 12 = 3 + 12

5. Warm-Up Exercises Solve an equation using division EXAMPLE 3 Solve –6x = 48. –6x = 48 x = –8 Write original equation. –6x –6 48 –6 = Divide each side by –6. Simplify.

6. Warm-Up Exercises GUIDED PRACTICE for Examples 1, 2, and 3 1. y + 7 = 10 ANSWER 3 Solve the equation. Check your solution.

7. Warm-Up Exercises 2. x – 5 = 3 GUIDED PRACTICE for Examples 1, 2, and 3 8 ANSWER Solve the equation. Check your solution.

8. Warm-Up Exercises GUIDED PRACTICE 3. q – 11 = –5 for Examples 1, 2, and 3 6 ANSWER Solve the equation. Check your solution.

9. Warm-Up Exercises GUIDED PRACTICE 4. 6 = t – 2 for Examples 1, 2, and 3 8 ANSWER Solve the equation. Check your solution.

10. Warm-Up Exercises GUIDED PRACTICE 5. 4x = 48 for Examples 1, 2, and 3 12 ANSWER Solve the equation. Check your solution.

11. Warm-Up Exercises GUIDED PRACTICE 6. –65 = –5y for Examples 1, 2, and 3 13 ANSWER Solve the equation. Check your solution.

12. Warm-Up Exercises GUIDED PRACTICE 7. 6w = –54 for Examples 1, 2, and 3 –9–9 ANSWER Solve the equation. Check your solution.

13. Warm-Up Exercises GUIDED PRACTICE 8. 24 = –8n for Examples 1, 2, and 3 –3–3 ANSWER Solve the equation. Check your solution.

14. Warm-Up Exercises Solve an equation using multiplication EXAMPLE 4 Write original equation. 4 x 4 = 4 5 Multiply each side by 4. x = 20 Simplify. = 5. x 4 Solve SOLUTION = 5 x 4

15. Warm-Up Exercises GUIDED PRACTICE for Example 4 9.9. = 9 t –3 Solve the equation. Check your Solution. –27 ANSWER

16. Warm-Up Exercises GUIDED PRACTICE for Example 4 10. 6 c 7 = Solve the equation. Check your Solution. 42 ANSWER

17. Warm-Up Exercises GUIDED PRACTICE for Example 4 11. 13 z –2 = Solve the equation. Check your Solution. –26 ANSWER

18. Warm-Up Exercises GUIDED PRACTICE for Example 4 12. = –11 a 5 Solve the equation. Check your Solution. –55 ANSWER

19. Warm-Up Exercises Solve an equation by multiplying by a reciprocal EXAMPLE 5 SOLUTION Write original equation. x = 4x = 4 2 7 – x = 4. 2 7 – Solve 7 2 – The coefficient of x is. 7 2 – The reciprocal of. 2 7 – is ( ) ( x ) = 2 7 – 7 2 – 7 2 – 4 2 Multiply each side by the 7 – reciprocal,.

20. Warm-Up Exercises Solve an equation by multiplying by a reciprocal EXAMPLE 5 x = –14 Simplify. ANSWER The solution is –14. Check by substituting –14 for x in the original equation. CHECK Write original equation. Substitute –14 for x. 4 = 4 Simplify. Solution checks. x = 4x = 4 2 7 – (–14) = 4 ? 2 7 –

21. Warm-Up Exercises GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. w = 10 5 6 13. ANSWER 12

22. Warm-Up Exercises GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. p = 14 2 3 14. ANSWER 21

23. Warm-Up Exercises GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. 15. 9 =9 = –3 4 m ANSWER –12

24. Warm-Up Exercises GUIDED PRACTICE for Example 5 Solve the equation. Check your Solution. 16. –8 = –4 5 v ANSWER 10

25. Warm-Up Exercises EXAMPLE 6 Write and solve an equation Let r represent Crawford's speed in meters per second. Write a verbal model. Then write and solve an equation. SOLUTION OLYMPICS In the 2004 Olympics, Shawn Crawford won the 200 meter dash. His winning time was 19.79 seconds. Find his average speed to the nearest tenth of a meter per second.

26. Warm-Up Exercises Write and solve an equation EXAMPLE 6 Crawford's average speed was about 10.1 meters per second. ANSWER 19.79200 19.79 r = 200 = r 19.79 10.1 r

27. Warm-Up Exercises GUIDED PRACTICE for Example 6 17. WHAT IF? In example 6, suppose Shawn Crawford ran 100 meters at the same average speed he ran the 200 meters. How long would it take him to run 100 meters ? Round your answer to nearest tenth of a second. 9.9 sec ANSWER

28. Warm-Up Exercises Daily Homework Quiz 2. 8 = m – 7 ANSWER 15 ANSWER 4 3. 9k = –72 ANSWER –8–8 1. –6 + a = –2 Solve the equation. Check your solution.

29. Warm-Up Exercises Daily Homework Quiz ANSWER –60 ANSWER 16.78 sec 4. 12 = x –5 5. Earth orbits the Sun at an average speed of 29.79 kilometers per second. Find how long it takes, to the nearest hundredth of a second, for Earth to travel 500 kilometers.

30. You will solve one-step equations using algebra. Essential Question: How do you solve one- step equations using subtraction, addition, division, and multiplication? Use inverse operations and properties of equality to produce equivalent equations and isolate variables. Use reciprocals to isolate a variable with a fractional coefficient. Solve one-step equations by using inverse operations to isolate the variable, for example, use addition to undo subtraction. If a coefficient is a fraction, multiply by its reciprocal to produce a coefficient of 1. Always perform the same operation on each side of the equation.