Answer
{$-\frac{7}{8}$}
Work Step by Step
$3x+5-5(x+1)= 6x+7$
$3x+5-5x-5=6x+7$
$3x-5x+5-5=6x+7$
$-2x=6x+7$
Subtracting 6x from both sides, $-2x-6x=6x+7-6x$
$-8x=7$
Dividing both sides by $-8$, $\frac{-8x}{-8}=\frac{7}{-8}$
Simplifying, $x= -\frac{7}{8}$
Therefore, the solution set is {$-\frac{7}{8}$}
Check:
Substituting $-\frac{7}{8}$ into the initial equation,
$3(-\frac{7}{8})+5-5(-\frac{7}{8}+1)= 6(-\frac{7}{8})+7$
$-\frac{21}{8}+5-5(\frac{1}{8})= -\frac{42}{8}+7$
$-\frac{21}{8}+5-\frac{5}{8}= -\frac{42}{8}+7$
$-\frac{26}{8}+5= -\frac{42}{8}+7$
$\frac{40-26}{8}=\frac{56-42}{8}$
$\frac{14}{8}=\frac{14}{8}$
$0=0$
Therefore, the answer checks out.
