## Calculus with Applications (10th Edition)

Published by Pearson

# Prerequisite Skills Diagnostic Test: 6

#### Answer

$x=\frac{-11}{5}$

#### Work Step by Step

Write out the equation $\frac{5}{8}x+\frac{1}{16}x=\frac{11}{16}+x$ Give $\frac{5}{8}x$ and $x$ the common denominator 16 by multiply by 1 ($\frac{2}{2}$ and $\frac{16}{16}$ respectively) $\frac{5}{8}x*\frac{2}{2}=\frac{10}{16}x$ $x*\frac{16}{16}=\frac{16}{16}x$ Insert back into equation $\frac{10}{16}x\frac{1}{16}x=\frac{11}{16}+\frac{16}{16}x$ Combine like terms $\frac{11}{16}x=\frac{11}{16}+\frac{16}{16}x$ $\frac{-5}{16}x=\frac{11}{16}$ Isolate x by multiply the entire equation by the reciprocal of $x$'s coefficient $\frac{16}{-5}(\frac{-5}{16}x=\frac{11}{16})$ $x=\frac{-11}{5}$

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