ANSWER 11b – 12 ANSWER Simplify the expression. 1.8b – 3(4 – b) 2.–6(m – 9) + 14m – 20...

ANSWER 11b – 12 ANSWER

Simplify the expression.

1. 8b – 3(4 – b) 2. –6(m – 9) + 14m – 20

8m + 34

ANSWER n + 0.05n, or 1.05n

3. You bought a pair of jeans for n dollars in a city where the sales tax rate is 5%. Write an expression for the total cost of the jeans, including sales tax.

EXAMPLE 1 Solve an equation with a variable on one side

Solve 45

x + 8 = 20.

45

x + 8 = 20

45

x = 12

x = (12)54

x = 15

Write original equation.

Subtract 8 from each side.

Multiply each side by , the reciprocal of .

544

5Simplify.

ANSWER The solution is 15.

CHECK x = 15 in the original equation.

45

45

x + 8 = (15) + 8 = 12 + 8 = 20

EXAMPLE 2 Write and use a linear equation

During one shift, a waiter earns wages of $30 and gets an additional 15% in tips on customers’ food bills. The waiter earns $105. What is the total of the customers’ food bills?

Restaurant

SOLUTION

Write a verbal model. Then write an equation. Write 15% as a decimal.

EXAMPLE 2 Write and use a linear equation

105 = 30 + 0.15x

75 = 0.15x

500 = x

Write equation.

Subtract 30 from each side.

Divide each side by 0.15.

The total of the customers’ food bills is $500.

ANSWER

GUIDED PRACTICE for Examples 1 and 2

Solve the equation. Check your solution.

1. 4x + 9 = 21

ANSWER The solution is x = 3.

2. 7x – 41 = – 13

ANSWER The solution is x = 4.

ANSWER The solution is -5.

3. 35

– x + 1 = 4

EXAMPLE 4 Solve an equation using the distributive property

Solve 3(5x – 8) = –2(–x + 7) – 12x.

3(5x – 8) = –2(–x + 7) – 12x

15x – 24 = 2x – 14 – 12x

15x – 24 = – 10x – 14

25x – 24 = –14

25x = 10

x = 25


Distributive property

Combine like terms.

Add 10x to each side.

Add 24 to each side.

Divide each side by 25 and simplify.

ANSWER The solution 25

EXAMPLE 4 Solve an equation using the distributive property

CHECK

25

3(5 – 8) –2(– + 7) – 12 25

25=?

3(–6) –14 – 45=? 24

5

– 18 = – 18

25

Substitute for x.

Simplify.

Solution checks.

GUIDED PRACTICE for Examples 3, 4, and 5


5. –2x + 9 = 2x – 7

ANSWER The correct answer is 4.

6. 10 – x = –6x + 15

ANSWER The correct answer is 1.

7. 3(x + 2) = 5(x + 4)

ANSWER The solution is –7.

GUIDED PRACTICE for Examples 3, 4, and 5


8. –4(2x + 5) = 2(–x – 9) – 4x

ANSWER The solution x = – 1

x + x = 3914

25

9.

ANSWER The correct answer is 60

EXAMPLE 1 Rewrite a formula with two variables

Solve the formula C = 2πr for r. Then find the radius of a circle with a circumference of 44 inches.

SOLUTION

C = 2πrC

2π = r

STEP 1 Solve the formula for r.

STEP 2Substitute the given value into the rewritten formula.

Write circumference formula.

Divide each side by 2π.

r = C2π = 44

2π 7 Substitute 44 for C and simplify.

The radius of the circle is about 7 inches.ANSWER

GUIDED PRACTICE for Example 1

The formula for the distance d between opposite vertices of a regular hexagon is d = where a is the distance between opposite sides. Solve the formula for a. Then find a when d = 10 centimeters.

2.2a3

SOLUTION

d 3a = 2

35When d = 10cm, a = or 8.7cm

EXAMPLE 2Rewrite a formula with three variables

SOLUTION

Solve the formula for w.STEP 1

P = 2l + 2w

P – 2l = 2w

P – 2l2 = w

Write perimeter formula.

Subtract 2l from each side.

Divide each side by 2.

Solve the formula P = 2l + 2w for w. Then find the width of a rectangle with a length of 12 meters and a perimeter of 41 meters.

EXAMPLE 2Rewrite a formula with three variables

41 – 2(12)2w =

w = 8.5

Substitute 41 for P and 12 for l.

Simplify.

The width of the rectangle is 8.5 meters.

ANSWER

Substitute the given values into the rewritten formula.

STEP 2


Solve the formula P = 2l + 2w for l. Then find the length of a rectangle with a width of 7 inches and a perimeter of 30 inches.

3.

Length of rectangle is 8 in.ANSWER

Solve the formula A = lw for w. Then find the width of a rectangle with a length of 16 meters and an area of 40 square meters.

4.

Write of rectangle is 2.5 mw = Al

ANSWER


Solve the formula for the variable in red. Then use the given information to find the value of the variable.

A = 12

bh5.Find h if b = 12 m

and A = 84 m2.

= h2A b

ANSWER


Find b if h = 3 cm


A = 12

bh6.

and A = 9 cm2.

= b2A h

ANSWER



A = 127. (b1 + b2)h Find h if b1 = 6 in.,

b2 = 8 in., and A = 70 in.2

h = 2A(b1 + b2)

ANSWER

EXAMPLE 3 Rewrite a linear equation

Solve 9x – 4y = 7 for y.

SOLUTION

Solve the equation for y.STEP 1

9x – 4y = 7

–4y = 7 – 9x

y = 94

74

– + x


Subtract 9x from each side.

Divide each side by –4.

EXAMPLE 4 Rewrite a nonlinear equation

Solve 2y + xy = 6 for y.

SOLUTION

Solve the equation for y.STEP 1

2y + x y = 6

(2+ x) y = 6

y = 62 + x


Distributive property

Divide each side by (2 + x).


Solve the equation for y. Then find the value of y when x = 2.

8. y – 6x = 7

y = 7 + 6x

y = 19

ANSWER

9. 5y – x = 13

y = x5

135 +

y = 3

ANSWER

10. 3x + 2y = 12

y = – 3x2 + 6

ANSWER

y = 3


Solve the equation for y. Then find the value of y when x = 2.

11. 2x + 5y = –1 12. 3 = 2xy – x 13. 4y – xy = 28

y = 14

284 – xy =

ANSWER

y = 1

41

3 +x 2xy =

ANSWER

2x5

–15 –

y = –1

y =

ANSWER

CLASSWORK

Workbook 1-3 (1-25 odd)Workbook 1-4 (1-25 odd)

ANSWER 11b – 12 ANSWER Simplify the expression. 1.8b – 3(4 – b) 2.–6(m – 9) + 14m – 20...

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