## Thinking Mathematically (6th Edition)

The solution set is $\varnothing$(the empty set
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