Question

no solutions.
-(-7x - 5) + 1 = 6 + 2(-6x + 3)

Explanation:

Step1: Simplify both sides

Left side: $-(-7x - 5)+1 = 7x + 5 + 1 = 7x + 6$
Right side: $6 + 2(-6x + 3)=6 - 12x + 6 = -12x + 12$

Step2: Solve for x

Set the simplified sides equal: $7x + 6 = -12x + 12$
Add $12x$ to both sides: $7x + 12x + 6 = 12$ → $19x + 6 = 12$
Subtract 6 from both sides: $19x = 12 - 6$ → $19x = 6$
Divide by 19: $x = \frac{6}{19}$

Wait, the original problem mentioned "no solutions," but our calculation shows a solution. Let's check the simplification again:

Left: $-(-7x -5)+1 = 7x +5 +1 = 7x +6$ (correct).
Right: $6 + 2(-6x +3) = 6 -12x +6 = -12x +12$ (correct).
Equation: $7x +6 = -12x +12$
$7x +12x = 12 -6$
$19x = 6$
$x = \frac{6}{19}$ (this is a valid solution, so the "no solutions" statement might be incorrect, or there was a typo in the problem.)

Answer:

The solution is $x = \frac{6}{19}$ (contradicts the "no solutions" claim; check the problem setup).