Algebra

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Worksheet by Kuta Software LLC

ID: 8

-1-

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Solve each equation.

1) 5 - 3(3r - 8) = 8r - 6(r + 8) 2)

2

7 =

7

3 a -

10

3 a

Solve each inequality, write its solution set in interval notation, and graph the solution set on a number line.

3) -5(1 + 2v) + 6(7v + 6) < 8v - 7v 4)

1

4 - 1

1

3 n £

9

4

Solve each compound inequality, write its solution set in interval notation, and graph the solution set on a number line.

5) 10 < 2p + 6 £ 20 6) -

3

2 < -

3

2 b <

3

2

Write the standard form of the equation of the line described.

7) through: (3, -2), perpendicular to y = 3 7 x - 3

Rewrite the equation in slope-intercept form and then use the slope and y-intercept to sketch a graph of the line with the given equation.

8) 9x + 4y = 16

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Worksheet by Kuta Software LLC

-2-

Show all work as you solve the linear modeling problem below.

9) Apple sold about 53 million iPods in 2008, but as iPhones became more popular, the sales of iPods began to decrease. The number of iPods sold in 2012 was about 33 million. Write a linear equation in slope-intercept form to model this decrease in sales. Let x stand for the number of years after 2008 and let y stand for the number of iPods sold, in millions.

Simplify. Your answer should contain only positive exponents.

10) 4yx5 × 2x3y4 11)

-4a-1 × -2a3b4

-4b2

12) (-x3y-1)3 13) (2x3y-2)3 × x5y3

Perform the indicated operation and simplify.

14) (5 - 4n - n2) - (7 - 8n2 + 6n)

Multiply as indicated and simplify.

15) (5a - 2)(3a2 - 7a + 5)

Solve the equation by factoring.

16) 3r2 = -7 + 22r

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Worksheet by Kuta Software LLC

-3-

Solve the equation by completing the square.

17) k2 - 6k - 7 = 3

Solve the equation by use of the quadratic formula.

18) 5v2 - 4v = 10

State the excluded values for the following expression. Then simplify the expression.

19) b2 - 81

b2 - 19b + 90

Solve the equation and show the check of the potential answer(s). If any answers are excluded values, state this on your answer sheet.

20) k + 3 k + 6

= 1 - 3

k2 + 8k + 12

Simplify the radical expressions.

21) 128x4yz3 22) (1 - 2 5 )(4 - 4 5 )

Solve the equation and show the check of the potential answer(s). If any answers are extraneous solutions, state this on your answer sheet.

23) -2 = 5b + 14 - b

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Worksheet by Kuta Software LLC

-4-

Show all work as you solve the following problems and write complete answers, including appropriate units.

24) Chelsea left the mall and traveled toward the ferry office. Two hours later Micaela left the mall traveling 28 km/h faster in an effort to catch up to her. After three hours Micaela finally caught up. What was Chelsea's average speed?

25) Maria put $42,000 in an education account on the day her daughter was born. If the account earned 4.45% interest compounded quarterly, what was the total in the account when her daughter turned 18? Round the final answer to the nearest cent.