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Test Bank for Algebra and Trigonometry Enhanced with Graphing Utilities , 7th Edition

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    Ch. 1 Graphs, Equations, and Inequalities 1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations 1 Use the Distance Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance d(P1, P2) between the points P1 and P2. 1) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) 41 B) 3 C) 10 D) 8 2) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 170 B) 6 2 C) 77 D) 4 Page 1

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    3) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 2 10 B) 32 2 C) 32 D) 4 4) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 5 5 B) 75 3 C) 75 D) 5 5) P1 = ( - 2, - 2); P2 = ( - 2, - 5) A) 3 B) 3 C) 4 D) 2 6) P1 = ( - 3, - 3); P2 = ( - 8, 9) A) 13 B) 169 C) 14 D) 26 7) P1 = (0, - 2); P2 = ( - 4, - 2) A) 4 B) 2 C) 2 5 D) 16 8) P1 = (0, 0); P2 = ( - 6, - 9) A) 3 13 B) 117 C) 15 D) 3i 6 9) P1 = (2, 1); P2 = ( - 2, - 6) A) 65 B) 33 C) 28 D) 3 10) P1 = (5, - 7); P2 = (3, - 3) A) 2 5 B) 12 3 C) 12 D) 6 Page 2

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    11) P1 = ( - 6, - 4); P2 = (4, - 6) A) 2 26 B) 96 6 C) 96 D) 12 12) P1 = ( - 0.9, - 0.2); P2 = (1.3, - 2.8) Round to three decimal places, if necessary. A) 3.406 B) 24 C) 10.77 D) 3.506 Decide whether or not the points are the vertices of a right triangle. 13) ( - 4, - 1), (5, - 1), (5, 4) A) Yes B) No 14) (8, 12), (10, 16), (12, 15) A) Yes B) No 15) ( - 5, - 8), (1, - 6), (0, - 11) A) Yes B) No 16) ( - 2, 9), (4, 11), (10, 4) A) Yes B) No Solve the problem. 17) Find all values of k so that the given points are 29 units apart. ( - 5, 5), (k, 0) A) - 3, - 7 B) - 7 C) 3, 7 D) 7 18) Find the area of the right triangle ABC with A = ( - 2, 7), B = (7, - 1), C = (3, 9). A) 29 square units B) 58 square units C) 58 2 square units D) 29 2 square units 19) Find all the points having an x - coordinate of 9 whose distance from the point (3, - 2) is 10. A) (9, 6), (9, - 10) B) (9, 2), (9, - 4) C) (9, - 12), (9, 8) D) (9, 13), (9, - 7) 20) A middle school's baseball playing field is a square, 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. A) 85 feet B) 86 feet C) 84 feet D) 92 feet 21) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find an expression for their distance apart in miles at the end of t hours. A) 52t miles B) t 68 miles C) 52 t miles D) 2t 13 miles 22) A rectangular city park has a jogging loop that goes along a length, width, and diagonal of the park. To the nearest yard, find the length of the jogging loop, if the length of the park is 125 yards and its width is 75 yards. A) 346 yards B) 146 yards C) 345 yards D) 145 yards Page 3

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    23) Find the length of each side of the triangle determined by the three points P1, P2, and P3. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. P1 = ( - 5, - 4), P2 = ( - 3, 4), P3 = (0, - 1) A) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 both B) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 isosceles triangle C) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 right triangle D) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 neither 2 Use the Midpoint Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the midpoint of the line segment joining the points P1 and P2. 1) P1 = (3, 8); P2 = (4, 1) A) ( 7 2 , 9 2 ) B) (7, 9) C) ( - 1, 7) D) ( 9 2 , 7 2 ) 2) P1 = (5, 4); P2 = (4, - 9) A) 9 2 , - 5 2 B) 1 2 , 13 2 C) 1, 13 D) 9, - 5 3) P1 = (7, 1); P2 = ( - 16, - 16) A) - 9 2 , - 15 2 B) 23 2 , 17 2 C) - 9, - 15 D) 9, 15 4) P1 = ( - 0.1, 0.7); P2 = ( - 2.5, - 1.5) A) ( - 1.3, - 0.4) B) ( - 0.4, - 1.3) C) ( - 1.2, - 1.1) D) ( - 1.1, - 1.2) 5) P1 = (b, 5); P2 = (0, 9) A) b 2 , 7 B) b, 14 C) - b 2 , 4 D) b, 7 6) P1 = (6x, 6); P2 = (7x, 5) A) 13x 2 , 11 2 B) 13x, 11 C) x, 1 D) 11x 2 , 13 2 Solve the problem. 7) If ( - 2, 4) is the endpoint of a line segment, and (2, 5) is its midpoint, find the other endpoint. A) (6, 6) B) (6, 3) C) ( - 10, 2) D) (0, 12) 8) If (1, 1) is the endpoint of a line segment, and ( - 4, - 2) is its midpoint, find the other endpoint. A) ( - 9, - 5) B) ( - 9, 4) C) (11, 7) D) ( - 5, - 9) 9) If (8, 2) is the endpoint of a line segment, and (11, 1) is its midpoint, find the other endpoint. A) (14, 0) B) (14, 3) C) (2, 4) D) (6, 8) Page 4

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    10) If ( - 3, - 2) is the endpoint of a line segment, and ( - 4, 0) is its midpoint, find the other endpoint. A) ( - 5, 2) B) ( - 5, - 4) C) ( - 1, - 6) D) (1, - 4) 11) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two - thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0). A) 2 17 3 B) 17 3 C) 2 D) 8 3 Page 5

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    3 Graph Equations by Plotting Points MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Plot the point in the xy - plane. Tell in which quadrant or on what axis the point lies. 1) (3, 5) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV Page 6

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    2) ( - 6, 1) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III Page 7

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    3) (2, - 4) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant I Page 8

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    4) ( - 5, - 1) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III B) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant III C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant IV D) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II Page 9

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    5) (0, - 6) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis B) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis Page 10

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    6) ( - 5, 0) x -5 5 y 5 -5 x -5 5 y 5 -5 A) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis B) x -5 5 y 5 -5 x -5 5 y 5 -5 y - axis C) x -5 5 y 5 -5 x -5 5 y 5 -5 Quadrant II D) x -5 5 y 5 -5 x -5 5 y 5 -5 x - axis Determine whether the given point is on the graph of the equation. 7) Equation: y = x 2 - x Point: (0, 0) A) Yes B) No 8) Equation: x 2 - y 2 = 64 Point: (8, 8) A) No B) Yes Page 11

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    Graph the equation by plotting points. 9) y = x - 2 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 12

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    10) y = 2x + 8 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 13

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    11) y = - x 2 + 1 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 14

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    12) 3x + 4y = 12 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 15

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    13) x 2 + 4y = 4 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 16

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    4 Graph Equations Using a Graphing Utility MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine the coordinates of the point shown. Tell in which quadrant the point lies. Assume the coordinates are integers. 1) A) ( - 4, 6); quadrant II B) ( - 4, 3); quadrant II C) ( - 4, 6); quadrant I D) ( - 4, 3); quadrant I Select a setting so that each of the given points will lie in the viewing window. 2) (8, 3), (5, 1), (9, 19) A) B) C) D) Page 17

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    Determine the viewing window used. 3) A) B) C) D) Page 18

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    Graph the equation using a graphing utility. 4) y = 2x + 1 A) B) C) D) 5) 2x - 3y = 3 A) B) C) D) Page 19

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    6) y = - 2x 2 + 9 A) B) C) D) 7) 3x 2 - 2y = 56 A) B) C) D) Page 20

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    5 Use a Graphing Utility to Create Tables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to create a table that displays the points on the graph of the given equation for x = - 3, - 2, - 1, 0, 1, 2, and 3. 1) y = 3x + 5 A) B) C) D) 2) 6x + 2y = 28 A) B) C) D) Page 21

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    3) y = - 3x 2 + 10 A) B) C) D) 4) 4x 2 - 2y = 16 A) B) C) D) Page 22

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    6 Find Intercepts from a Graph MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List the intercepts of the graph. 1) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) ( - 1, 0), (1, 0) B) (0, - 1), (1, 0) C) (0, - 1), (0, 1) D) ( - 1, 0), (0, 1) 2) x -5 5 y 5 -5 x -5 5 y 5 -5 A) (0, - 1) B) (0, 0) C) ( - 1, - 1) D) ( - 1, 0) Page 23

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    3) x -  -  2  2  y 5 4 3 2 1 -1 -2 -3 -4 -5 x -  -  2  2  y 5 4 3 2 1 -1 -2 -3 -4 -5 A) - π 2 , 0 , (0, 3), π 2 , 0 B) - π 2 , 0 , (3, 0), π 2 , 0 C) 0, - π 2 , (3, 0), 0, π 2 D) 0, - π 2 , (0, 3), 0, π 2 4) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) ( - 4, 0), (0, 8), (2, 0) B) ( - 4, 0), (0, 8), (0, 2) C) (0, - 4), (8, 0), (0, 2) D) (0, - 4), (0, 8), (2, 0) 5) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) ( - 4, 0) B) (0, - 4) C) (4, 0) D) (0, 4) Page 24

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    6) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) ( - 7, 0), (0, - 7), (0, 7), (7, 0) B) ( - 7, 0), (0, 7) C) ( - 7, 0), (0, - 7), (0, 0), (0, 7), (7, 0) D) (0, 7), (7, 0) 7) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) (4, 0), (1, 0) (5, 0), (0, - 4) B) ( - 4, 0), (0, 4), (0, 1), (0, 5) C) ( - 4, 0), (1, 0), ( - 5, 0), (0, - 4) D) ( - 4, 0), (0, - 4), (0, 1), (0, - 5) 8) A) ( - 4, 0), (0, 4), (4, 0) B) ( - 2, 0), (0, 2), (2, 0) C) ( - 2, 0), (0, 4), (2, 0) D) ( - 2, 0), (2, 0) Page 25

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    7 Use a Graphing Utility to Approximate Intercepts MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places, if necessary. Use the TABLE feature to help establish the viewing window. 1) y = - 2x + 15 A) (0, 15), (7.5, 0) B) (0, 15), ( - 7.5, 0) C) (0, - 15), (7.5, 0) D) (0, 15), ( - 7.5, 0), (7.5, 0) 2) y = - 4x + 15 A) (0, 15), (3.75, 0) B) (0, 3.75), (15, 0) C) (0, 15), ( - 3.75, 0) D) (0, - 3.75), (15, 0) 3) y = 3x 2 - 19 A) (0, - 19), ( - 2.52, 0), (2.52, 0) B) (0, - 19), (2.52, 0) C) (0, 19), ( - 2.52, 0), (2.52, 0) D) (0, - 19), ( - 2.51, 0), (2.51, 0) 4) y = 5x 2 - 13 A) (0, - 13), (1.61, 0), ( - 1.61, 0) B) (0, 1.61), (0, - 1.61), ( - 13, 0) C) (0, - 13), (2.60, 0), ( - 2.60, 0) D) (0, 2.60), (0, - 2.60), ( - 13, 0) 5) 3x - 4y = 56 A) (0, - 14), (18.67, 0) B) (0, - 14), (18.66, 0) C) (0, - 14), ( - 18.67, 0), (18.67, 0) D) (0, 14), (18.67, 0) 6) 6x - 5y = 67 A) (0, - 13.40), (11.17, 0) B) (0, 11.17), ( - 13.40, 0) C) (0, 13.40), ( - 11.17,0) D) (0, - 13.41), (11.18, 0) 7) 3x 2 - 5y = 34 A) (0, - 6.8), ( - 3.37, 0), (3.37, 0) B) (0, - 6.8), ( - 3.36, 0), (3.36, 0) C) (0, 6.8), ( - 3.37, 0), (3.37, 0) D) (0, - 6.8), (3.37, 0) 8) 4x 2 - 5y = 68 A) (0, - 13.60), (4.12, 0), ( - 4.12, 0) B) (0, 4.12), (0, - 4.12), ( - 13.60, 0) C) (0, - 13.59), (4.13, 0), ( - 4.13, 0) D) (0, 13.60), (4.12, 0), ( - 4.12, 0) 1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations 1 Solve Equations Using a Graphing Utility MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to approximate the real solutions, if any, of the equation rounded to two decimal places. 1) x 3 - 6x + 3 = 0 A) {2.15, 0.52, - 2.67} B) { - 0.48} C) {2.67, - 0.52, - 2.15} D) no solution 2) x 4 - 3x 2 + 4x + 15 = 0 A) { - 0.84, - 1.93} B) {2.11, - 2.60} C) {3.94, - 1.27} D) no solution 3) 2x 4 - 5x 2 + 7x = 14 A) { - 2.31, 1.69} B) { - 2.31, 1.70} C) { - 2.30, 1.69} D) { - 2.32, 1.70} Page 26

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    4) x 4 - 5x 3 + 6x - 2 = 0 A) {4.75, 1, 0.38, - 1.13} B) {0.31, - 5.23} C) {4.71, 1.44, - 0.38, - 0.77} D) no solution 5) - x 4 + 3x 3 + 4 3 x 2 = 9 2 x + 2 A) {2.82, 1.61, - 0.46, - 0.97} B) { - 3.34} C) {1.09, - 0.44} D) no solution 2 Solve Linear Equations MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) 4x = - 24 A) { - 6} B) {6} C) {4} D) { - 4} 2) 9x = 12 A) 4 3 B) - 4 3 C) 3 4 D) - 3 4 3) 2x + 6 = 0 A) { - 3} B) {3} C) {2} D) { - 2} 4) 5x - 10 = 0 A) 2 B) - 2 C) 1 2 D) - 1 2 5) 7x + 2 = 0 A) - 2 7 B) 2 7 C) 7 2 D) - 7 2 6) 1 2 x = - 5 9 A) - 10 9 B) - 9 10 C) 10 9 D) 10 3 7) 13x = - 13 + 12x A) { - 13} B) {13} C) { - 12} D) { - 1} 8) 10x - 18 = 4x + 30 A) {8} B) { - 8} C) {5} D) { - 5} 9) - 3x - 49 = 4x + 7 A) { - 8} B) {8} C) { - 7} D) {7} 10) 35 - 2x = - 14 + 5x A) {7} B) { - 7} C) {5} D) { - 5} 11) 7x - (2x - 1) = 2 A) 1 5 B) 1 9 C) - 1 5 D) - 1 9 Page 27

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    12) 3(4x - 1) = 12 A) 5 4 B) 3 4 C) 13 12 D) 11 12 13) 14(5x - 2) = 9x - 7 A) 21 61 B) 35 61 C) - 21 61 D) 21 79 14) 6(x + 5) = 7 x - (3 - x) A) 51 8 B) - 15 4 C) 15 4 D) - 51 8 15) 3(x + 2) = 4(x - 8) A) {38} B) { - 38} C) { - 26} D) {4} 16) 4(2x - 2) = 7(x + 5) A) {43} B) { - 27} C) { - 43} D) {31} 17) 3(x + 4) = (3x + 12) A) {24} B) {0} C) all real numbers D) no solution 18) - 5x - 6 - 7(x + 1) = 7x + 2 A) - 15 19 B) - 5 8 C) 3 10 D) {7} 19) - 9x + 6 + 7x = - 2x + 11 A) {5} B) { - 6} C) all real numbers D) no solution 20) x 2 - 4 = 1 A) {10} B) { - 10} C) {6} D) { - 6} 21) x 2 - 1 2 = - 3 A) { - 5} B) {5} C) { - 7} D) {7} 22) 2x 5 = 2 + x 3 A) {30} B) { - 30} C) {60} D) { - 60} 23) x 3 + 1 = x 4 + 3 A) 24 B) - 24 C) 1 6 D) - 1 6 24) 1 5 - x 2 = 17 10 A) - 3 B) 3 C) - 15 2 D) 15 2 Page 28

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    25) - 9.6x + 1.7 = - 83 - 1.9x A) {11} B) { - 92} C) {8.8} D) {9} 26) - 3x + 5 7 + 3 7 = - 7x 3 A) - 3 5 B) - 3 20 C) 3 20 D) 12 29 27) (x + 2)(x - 1) = (x + 1) 2 A) - 3 B) - 2 C) 3 2 D) {3} 28) x(3x - 4) = (3x + 1)(x - 2) A) - 2 B) - 1 C) 2 D) {5} 29) x(1 + 3x) = (3x - 1)(x - 3) A) 3 11 B) - 3 11 C) 3 121 D) - 3 121 30) x(x 2 + 4) = 9 + x 3 A) 9 4 B) {4} C) {9} D) 4 9 Solve the problem. 31) If (a, 3) is a point on the graph of y = 2x - 5, what is a? A) 4 B) 1 C) - 1 D) - 4 32) If (3, b) is a point on the graph of 3x - 2y = 17, what is b? A) - 4 B) 4 C) 23 3 D) 11 3 Solve the equation. The letters a, b, and c are constants. 33) ax - b = c, a ≠ 0 A) x = b + c a B) x = b - c a C) x = c - b a D) x = - b + c a 34) x a + x b = c, a ≠ 0, b ≠ 0, a ≠ - b A) x = abc a + b B) x = abc C) x = c ab D) x = a + b abc 3 Solve Rational Equations MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) 1 - 3 4x = 2 A) - 3 4 B) 3 4 C) - 12 7 D) - 7 4 Page 29

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    2) 5 x + 2 5 = 7 x A) {5} B) { - 5} C) {2} D) { - 2} 3) - 8 x + 5 x = 5 A) - 3 5 B) - 5 3 C) 3 5 D) 5 3 4) 3 x + 5 + 2 2x + 1 = 4 x - 2 A) - 46 47 B) 46 47 C) - 47 46 D) 47 46 5) 5 - x x + 3 4 = 7 x A) { - 8} B) - 8 7 C) {8} D) { - 4} 6) x x - 9 - 4 = 9 x - 9 A) {9, - 9} B) {9} C) { - 9} D) no solution 7) x 2x + 2 = 2x - 3 x + 1 - 2x 4x + 4 A) {3} B) 3 2 C) { - 3} D) no solution 8) 1 x + 1 x + 6 = x + 7 x + 6 A) {1} B) { - 6} C) { - 1} D) {6} 9) 6 2x - 3 = 4 2x + 5 A) - 21 2 B) 21 2 C) - 2 21 D) 2 21 10) 2x x 2 - 4 = 1 x 2 - 4 - 4 x + 2 A) 3 2 B) - 7 6 C) 7 2 D) - 3 8 11) x - 2 x - 5 = x + 6 x - 7 A) 22 5 B) - 15 7 C) { - 4} D) 8 5 Page 30

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