3.1

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Solve One-Step Equations

3.1 Warm-Up

Solve using mental math.

1. x + 2 = 17

ANSWER 15

ANSWER 24

2. x6 = 4

3. x – 7 = 3

ANSWER 10

ANSWER 6

4. 9x = 54

3.1 Warm-Up

5. Katrina divided her photos into three albums. Each album contains 26 photos. How many photos did Katrina have to begin with?

ANSWER 78 photos

3.1 Example 1

Solve x + 7 = 4.

x + 7 = 4 Write original equation.

x + 7 – 7 = 4 – 7 Use subtraction property of equality: Subtract 7 from each side.

x = –3 Simplify.

ANSWERThe solution is –3.

3.1 Example 1

CHECK Substitute –3 for x in the original equation.

x + 7 = 4 Write original equation.

–3 + 7 = 4? Substitute –3 for x.

4 = 4 Simplify. Solution checks.

3.1 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 + 12

x = 15 Simplify. x = 15

x – 12 + 12 = 3 + 12

3.1 Example 3

Solve –6x = 48.

–6x = 48

x = –8

Write original equation.

–6x–6

48–6= Divide each side by –6.

Simplify.

3.1 Guided Practice

1. y + 7 = 10

ANSWER 3

Solve the equation. Check your solution.

2. x – 5 = 3

8ANSWER

3. q – 11 = –5

6ANSWER

4. 6 = t – 2

8ANSWER

5. 4x = 48

12ANSWER

6. –65 = –5y

13ANSWER

7. 6w = –54

–9ANSWER

8. 24 = –8n

–3ANSWER

3.1 Example 4

Write original equation.

4 x4 = 4 5 Multiply each side by 4.

x = 20 Simplify.

= 5.x 4Solve

SOLUTION

= 5x4

3.1 Guided Practice

9. = 9t–3

Solve the equation. Check your solution.

–27ANSWER

12. = –11a 5

–55ANSWER

10. 6 c7=

42ANSWER

11. 13 z–2=

–26ANSWER

3.1 Example 5

SOLUTION

Write original equation.x = 427

–

x = 4.27

–Solve

72–The coefficient of x is .

72

–The reciprocal of .27

–is

( )(x ) =27

–72

–72

– 4

2

Multiply each side by the 7

–reciprocal, .

x = –14 Simplify.

3.1 Example 5

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 = 427

–

(–14) = 4 ?2

7–

3.1 Guided Practice

Solve the equation. Check your solution.

w = 105613.

ANSWER 12

p = 142314.

ANSWER 21

15. 9 = –3

4m

ANSWER –12

16. –8 = –4

5v

ANSWER 10

3.1 Example 6

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.

3.1 Example 6

Crawford's average speed was about 10.1 meters persecond.

ANSWER

19.7920019.79 19.79 r=

200 = r 19.79

10.1 r

3.1 Guided Practice

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 torun 100 meters? Round your answer to nearest tenth of a second.

9.9 secANSWER

3.1 Lesson Quiz

2. 8 = m – 7

ANSWER 15

ANSWER 4

3. 9k = –72

ANSWER –8

1. –6 + a = –2Solve the equation. Check your solution.

ANSWER –60

4. 12 = x–5

3.1 Lesson Quiz

ANSWER 16.78 sec

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.