Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 5 - Linear Functions - 5-1 Rate of Change and Slope - Standardized Test Prep: 61

Answer

a) $20 < 2x +16 < 30$ b) $ 2 < x < 7$, please see the first graph. c) $2/3 < x < 10$, please see the second graph.
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Work Step by Step

a) Two of the sides of the rectangle have lengths of (x+2) and 6. Since these sides are not parallel, the other two sides have sides of the same length. $20< (x+2) + (x+2) + 6 + 6 < 30$ $20 < 2x +16 < 30$ b) $20 < 2x +16 < 30$ $20 -16 < 2x + 16 - 16 < 30-16$ $4 < 2x < 14$ $4/2 < 2x/2 < 14/2$ $2 < x < 7$ c) possible pairs of triangle legs: (6, x+4), (6, 2x), (2x,x+4) $6 + x+4 > 2x$ $10 + x > 2x$ $10 + x - x > 2x - x $ $10 > x $6 + 2x > x + 4$ $6 + 2x - x - 4 > x + 4 - x - 4$ $2 + x > 0$ $2 + x - 2 > 0 - 2$ $x > -2 $ $x+4 + 2x > 6$ $3x + 4 > 6$ $3x + 4 - 4 > 6 - 4 $ $3x > 2 $ $3x/3 > 2/3$ $x > 2/3$ If we let x = 11, we would not have a triangle as the lengths would be 6, 15, and 22 (and 6 + 15 < 22). Thus, the solution set is 2/3 < x < 10.
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