Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - Chapter Review Exercises - Page 670: 66

Answer

$x = \frac{11}{3}$ To check if our solution is correct, substitute it back into the original equation: $\sqrt {3(\frac{11}{3}) - 7} = 2$ Multiply factors within the radical: $\sqrt {11 - 7} = 2$ Simplify the radical: $\sqrt {4} = 2$ Evaluate the square root: $2 = 2$ The two sides are equal; therefore, the solution is correct.

Work Step by Step

Square both sides of the equation: $3x - 7 = 2^{2}$ Evaluate the right side of the equation: $3x - 7 = 4$ Add $7$ to each side of the equation to solve for $x$: $3x = 11$ Divide both sides of the equation by $3$: $x = \frac{11}{3}$ To check if our solution is correct, substitute it back into the original equation: $\sqrt {3(\frac{11}{3}) - 7} = 2$ Multiply factors within the radical: $\sqrt {11 - 7} = 2$ Simplify the radical: $\sqrt {4} = 2$ Evaluate the square root: $2 = 2$ The two sides are equal; therefore, the solution is correct.
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