Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1 - Introduction to Algebraic Expressions - 1.3 Fraction Notation - 1.3 Exercise Set: 87

Answer

The two equations are not equal to each other because 0 is the only viable solution.

Work Step by Step

To see if $\frac{2+x}{8}$ and $\frac{1+x}{4}$ are equal, try to solve for an equation in which the two expressions are equal, as shown below. $(2+x)\div8=(1+x)\div4$ $((2+x)\div8)\times8=((1+x)\div4)\times8$ $2+x=2+2x$ $(2+x)-2=(2+2x)-2$ $x=2x$ As shown below, unless $x=0$, the two expressions are not equal. For the two to be equal, they have to be the same no matter the variable.
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