Answer
{$-\frac{6}{11}$}
Work Step by Step
Step 1: $5(x+3)+4x-3=-(2x-4)+2$
Step 2: $5x+15+4x-3=-2x+4+2$
Step 3: $9x+12=-2x+6$
Step 4: Adding $2x$ to both sides, $9x+2x+12=-2x+6+2x$
Step 5: $11x+12=6$
Step 6: Subtracting 12 from both sides, $11x+12-12=6-12$
Step 7: $11x=-6$
Step 8: Dividing both sides by $11$, $\frac{11x}{11}=\frac{-6}{11}$
Step 9: Simplifying, $x= -\frac{6}{11}$
Step 10: Therefore, the solution set is {$-\frac{6}{11}$}
Check:
Substituting $-\frac{6}{11}$ into the simplified equation of Step 3,
$9(\frac{-6}{11})+12=-2(\frac{-6}{11})+6$
$(\frac{-54}{11})+12=(\frac{12}{11})+6$
$\frac{132-54}{11}=\frac{66+12}{11}$
$\frac{78}{11}=\frac{78}{11}$
$0=0$
Therefore, the answer checks out.
