Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 363: 99


The solution set is \[\varnothing \](the empty set

Work Step by Step

The equation is \[5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right]\]. Use the order of operations, Work inside parentheses first, \[\begin{align} & 5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right] \\ & 5-12x=8-7x-\left[ 6\div 3\left( 2+125 \right)+5x \right] \\ & 5-12x=8-7x-\left[ 6\div 3\times 127+5x \right] \\ & 5-12x=8-7x-\left[ 2\times 127+5x \right] \end{align}\] \[\begin{align} & 5-12x=8-7x-\left[ 254+5x \right] \\ & 5-12x=8-7x-254-5x \\ & 5-12x=-246-12x \\ \end{align}\] Add \[12x\] to both sides of the equal sign, \[\begin{align} & 5-12x+12x=-246-12x+12x \\ & 5=-246 \end{align}\] Therefore, the equation\[5-12x=8-7x-\left[ 6\div 3\left( 2+{{5}^{3}} \right)+5x \right]\]is equivalent to the statement \[5=-246\]. Which is false for every value of \[x\]. Thus, the equation has no solution. The solution set is \[\varnothing \](the empty set
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