Solve each equation.

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1. 3d + 8 = 2d - 17

2.) 2n - 7 = 5n - 10

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3) -v + 5 + 6v = 1 + 5v + 3

4) 5(r - 1) = 2(r - 4) - 6

Solve for indicated variable.

5) 4c = d for c

6) 2p + 5r = q for p

7) - 10 = xy + z for x

8) _{for j}

Solve each equation.

9) |x| = 12

10) |x - 1| = 2

11) 3|x| = 24

12) 4|x - 5| = 12

13) How many solutions does the equation |x + 7| = 1 have?

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14) How many solutions does the equation |x + 7| = 0 have?

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15) How many solutions does the equation |x + 7| = - 1 have?

Solve each inequality and graph the solutions.

16) b + 8 > 15

17) -9 ≥ m - 9

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18) -7y < 21

19) 2s ≤ - 3

20)

21)

22) -3a + 10 < - 11

23) 6(n - 8) ≥ - 18

24) 2x + 30 ≥ 7x

25) 5s - 9 < 2(s - 6)

Write the compound inequality shown by each graph.

26)

27)

Solve each compound inequality and graph the solutions.

28) 12 ≤ 4n < 28

29) x - 3 < -3 OR x - 3 ≥ 3

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30) - 2 ≤ 3b + 7 ≤ 13

31) 5k ≤ -20 OR 2k ≥ 8

Solve each inequality and graph the solutions.

32) |x| - 2 ≤ 3

33) |x + 3| - 1.5 < 2.5

34) |x| + 17 > 20

35) 2|x - 2| ≥ 3

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Evaluate each function for the given input values

36) For f(x) = 5x + 1, find f(x)

when x = 2 and x = 3

37) For h(x) = x - 3, find h(x)

when x = 3 and x = 1

Use x- and y-intercepts to graph the equation.

38) 3x + 2y = - 6

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Find the slope of each line.

39)

40)

41)

42)

Find the slope of the line that contains each pair of points.

43) (2,8) and (1,-3)

44) (0,-2) and (4,-7)

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Find the slope of the line described by each equation.

45) 3x + 4y = 24

46) 8x + 48 = 3y - 44)

Write the equation that describes each line in slope-intercept form.

47) slope = 4; y-intercept = -3

48) slope = -⅓; y-intercept = 6

49) slope = ⅖; (10, 3) is on the line

50) slope = -⅓ ; (- 6, 0) is on the line

51) see next page

52) see next page

Write the equation in point-slope form for the line with the given slope and point.

53) slope = 3; (-4, 2) is on the line

54) slope = -1; (6, -1) is on the line

55) see next page

56) see next page

57) slope = -4; (1, -3) is on the line

58) (2,1) and (0, -7) are on the line.

Write each equation in slope-intercept form. Then graph the line.

51) y + x = 3

52) 5x - 2y = 10

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Find the x- and y- intercepts of the line that contains each pair of points.

55) y + 2 = - ⅔ (x - 6)

56) y + 3 = -2(x - 4)

Find the x- and y-intercepts of the line that contains each pair of points.

59) (-1, -4) and (6, 10)

60) (3, 4) and (-6 , 16)

Identify which lines are parallel.

61)

y = 3x + 4

y = 4

y = 3x

y = 3

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Identify which lines are perpendicular.

62)

y = -2

y = -½ x - 4

y - 4 = 2(x + 3)

y = -2x

Determine whether the ordered pair is a solution of the given system.

63) ( 3, 1); {

64) (6, -2); {

Solve each system by graphing.

65) Solution: __________

y = x + 4

y = -2x + 1

66) Solution: ___________

y = x + 6

y = -3x + 6 _____

Solve each system by substitution.

67) y = x -2; y = 4x + 1

68) y = x - 4; y = -x + 2

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69) 2x - y = 6; x + y = -3

70) 2x + 3y = 0; x + 2y = -1

71) -2x + y = 0; 5x + 3y = -11

72) ½ x + ⅓ y = 5; ¼ x + y = 10

Solve each system by the elimination method (also known as the addition/subtraction method)

73) 2x - 3y = 14; 2x + y = -10

74) 3x + y = 17; 4x + 2y = 20

75) x + 3y = -7; - x + 2y = -8

76) x + 3y = -14; 2x - 4y = 32

77) y - 3x = 11; 2y - x = 2

78) -10x + y = 0; 5x + 3y = -7

Solve each system of linear equations. (Choose your method.)

79) y = 2x - 3; y - 2x = -3

80) y - x + 3 = 0; x = y + 3

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Determine whether the ordered pair is a solution of the given inequality.

81) (1,6); y < x + 6

82) (5, -3); y ≤ -x + 2

Graph the solutions of each linear inequality.

83) y ≤ x + 4

84) 2x + y > -2

Write an inequality to represent each graph.

85)

86)

Determine whether the ordered pair is a solution of the given system.

87) (2, -2); {

88) (1, 3); {

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Graph the system of linear inequalities.

1. Give two ordered pairs that are solutions.
2. Give two ordered pairs that are not solutions.

89)

y ≤ x + 4

y ≥ -2x

90)

y ≤ ½ x + 1

x + y < 3

Simplify.

91) 3⁰

92) 3 ^{- 3}

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93) - 3 ^{- 4} 93.5) (-3)^-4

94) (4.2)⁰

Evaluate each expression for the given value(s) of the variable(s).

95) (2t)^{- 3} for t = 2

96) 2x⁰y ^{- 3} for x = 7 and y = -4

Rewrite so there are no negative exponents.

97) 3k ^{- 4}

98) x¹⁰/d ^{- 3}

99) f ^{- 4}/g ^{- 6}

100) p⁷q ^{- 1}

Add or subtract

115) 13x² + 9y² - 6x²

116) - 8m² + 5 - 16 + 11m

117) (9x⁴ + x³ ) + (2x⁴ + 6x³ - 8x⁴ + x³)

118) (3.7q² - 8q + 3.7) + (4.3q³ - 2.9q + 1.6)

119) (2r + 5) - (5r - 6)

120) (-7k² + 3 ) - (2k² + 5k - 1)

Multiply.

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121) (-5mn³)(4m²n²)

122) (2pq³)(5p²q²)(-3q⁴)

123) -3x(x² - 4x + 6)

124) (y - 3)(y - 5)

125) (m² - 2mn)(3mn + n²)

126) (3x + 4)(x² - 5x + 2)

127) (-4x + 6)(2x³ - x² + 1)

128) (a + b)(a - b)(b - a)

129) (2 + x)²

130) (2x + 6)²

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131) (2a + 7b)²

132) (x - 2)²

Find the GCF of each pair of monomials.

133) 6x² and 5x²

134) 13q⁴ and 2p²

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Factor each polynomial using GCF

135) 10g³ - 3g

136) -4x² - 6x

137) 3x² - 9x +3

138) 14n³ + 7n +7n²

Factor each expression.

139) 5(m - 2) - m(m - 2)

140) 4(x - 3) - x(y + 2)

Factor each polynomial by grouping.

141) 6x³ + 4x² + 3x +2

142) 2m³ + 4m² +6m + 12

143) 3r - r² + 2r - 6

144) 6a³ - 9a² - 12 + 8a

Factor.

145) x² + 13x + 36

146) x² + 10x + 16

147) x² - 11x + 24

148) x² - 7x + 6

149) x² + 3x - 88

150) x² + 6x - 27

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151) x² - x - 2

152) x² - 4x - 45

153) 2x² + 9x + 10

154) 5x² + 7x - 6

155) 7x² - 3x - 10

156) 2y² - 11y + 14

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157) - 4n² - 16n + 9

158) - 6x² + 13x - 2

159) x² - 4x + 4

160) 9x² - 12x + 4

161) x² + 2x + 1

162) x² - 6x - 9

163) 1 - 4x²

164) 81x² - 1

165) 4x⁴ - 9y²

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Factor each polynomial completely.

167) 2(4x³ - 3x² - 8x)

168) 4(4p⁴ - 1)

169) 3x⁵ - 12x³

170) 8pq² + 8pq + 2p

171) mn⁵ - m³n

172) 6x⁴ - 3x³ - 9x²

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173) p⁵ + 3p³ + p² + 3

174) 2z² - 11z + 6

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Write a mathematical expression for each.

175) A number doubled plus seven

176) Six less than five times a number

177) Five times the quantity of a number plus three.

178) The quotient of a number and ten

179) The sum of sixteen and a number

180) Four subtracted from a number and then multiplied by two

181) Kali left school and traveled toward her friend's house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.

182) A car started out from Seattle toward Vancouver at the rate of 60 km/h. A second car left from the same point 2 hours later and drove along the same route, but at 75 km/h. How long did it take the second car to overtake the first car?

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183) The perimeter of a triangle is 69 cm. Side a is 5 cm shorter than side b. Side c is twice as long as side a. Find the length of each side.

184) Graph y = - x² + 7x - 6

Solve.

185)

= 0

186) Simplify:

187)

188)

189)

190)

Simplify and Rationalize (if necessary)

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191)

192)

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193)

194)

195)

196)

197)

198)

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Solve.

199)

200)

= 12

201)

202)

203)

204)

205) Solve twice - once using the quadratic formula and once using factoring. 3x² - 8x - 3 = 0

206) Solve twice - once using the quadratic formula and once using factoring.