4. solve for x: -2(x - 2) + 6 = -4(x + 4)

Explanation:

Step1: Expand both sides

Expand -2(x - 2) to -2x + 4 and -4(x + 4) to -4x - 16. The equation becomes -2x + 4+6=-4x - 16.

Step2: Simplify the left - hand side

Combine like terms on the left - hand side: -2x+(4 + 6)=-2x + 10. So the equation is -2x + 10=-4x - 16.

Step3: Add 4x to both sides

-2x+4x + 10=-4x+4x - 16, which simplifies to 2x + 10=-16.

Step4: Subtract 10 from both sides

2x+10 - 10=-16 - 10, resulting in 2x=-26.

Step5: Divide both sides by 2

$\frac{2x}{2}=\frac{-26}{2}$, so x=-13.

Answer:

x = - 13