Prerequisite Skills Pg. 130 #1-13

Copy and complete the statement.

ANSWER 85

ANSWER 3x, 7x

1. In the expression 3x + 7 + 7x, and are like terms.

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2. The reciprocal of is .58

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Prerequisite Skills SKILLS CHECK

Simplify the expression.

3. 5x – (6 – x)

4. 3(x – 9) – 16

5. 23 + 4(x + 2)

6. x(7 + x) + 9x2

ANSWER 6x – 6

ANSWER 3x – 43

ANSWER 4x + 31

ANSWER 10x2 + 7x

Write the percent as a decimal.

7. 54% ANSWER 0.54

8. 99% ANSWER 0.99

9. 12.5% ANSWER 0.125

10. 150% ANSWER 1.5

Prerequisite Skills

Find the perimeter of the rectangle.

ANSWER 46 ft

ANSWER 68 cm

ANSWER 30 in.

11.

12.

13.

SKILLS CHECK

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Modeling One-Step Equations

Vocabulary• Golden Rule of Algebra:

Do unto one side what you do to the other!!!• Inverse Operations:

– Examples:

• Properties to solve equations:

1.) Addition Property of Equality:

2.) Subtraction Property of Equality:

3.) Multiplication Property of Equality:

4.) Division Property of Equality:

adding the same # to each side produces an equivalent equation

subtracting the same # to each side produces an equivalent equation

multiplying the same # to each side produces an equivalent equation

dividing the same # to each side produces an equivalent equation

2 operations that UNDO each other

add & subtract; multiply & divide

Solve an equation using subtractionEXAMPLE 1

Solve x + 7 = 4.

– 7 – 7Use subtraction property of equality: Subtract 7 from each side.

x = –3 Simplify.

ANSWER The solution is –3.

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.

Solve an equation using addition

EXAMPLE 2 & 3

Solve x – 12 = 3.Add 12 to each side.+ 12 + 12Simplify.x = 15

Solve –6x = 48.

x = –8

–6x–6

48–6= Divide each side by –6.

Simplify.

GUIDED PRACTICE for Examples 1, 2, and 3

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

Solve an equation using multiplicationEXAMPLE 4

4 x4 = 4 5 Multiply each side by 4.

x = 20 Simplify.

= 5.x 4Solve

SOLUTION

GUIDED PRACTICE for Example 4

9. = 9t–3

Solve the equation. Check your Solution.

–27ANSWER

10. 6 c7= 42ANSWER

11. 13 z–2= –26ANSWER

12. = –11a 5 –55ANSWER

Solve an equation by multiplying by a reciprocal

EXAMPLE 5

SOLUTION

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.ANSWER

The solution is –14. Check by substituting –14 for x in the original equation.

CHECK Substitute –14 for x.

4 = 4 Simplify. Solution checks.

(–14) = 4 ?

27

–

GUIDED PRACTICE for Example 5

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

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.

19.7920019.79 19.79 r=

200 = r 19.79

10.1 r

Crawford's average speed was about 10.1 meters persecond.

ANSWER

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

9.9 secANSWER

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Box Jellyfish

Check Yourself

Pg. 137-140 #4-28eoe, 30-48e, 55, 61, 64-66