Sure! Let's solve the equation step-by-step:
Given the equation:
[tex]\[ -4(x - 2) + 2x = 16 \][/tex]
1. Distribute the [tex]\(-4\)[/tex] across the [tex]\((x - 2)\)[/tex]:
[tex]\[ -4 \cdot x + (-4) \cdot (-2) + 2x = 16 \][/tex]
This simplifies to:
[tex]\[ -4x + 8 + 2x = 16 \][/tex]
2. Combine like terms on the left side:
Group the [tex]\(x\)[/tex] terms together:
[tex]\[ (-4x + 2x) + 8 = 16 \][/tex]
This simplifies to:
[tex]\[ -2x + 8 = 16 \][/tex]
3. Isolate the terms involving [tex]\(x\)[/tex] by subtracting 8 from both sides:
[tex]\[ -2x + 8 - 8 = 16 - 8 \][/tex]
This simplifies to:
[tex]\[ -2x = 8 \][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(-2\)[/tex]:
[tex]\[ x = \frac{8}{-2} \][/tex]
This simplifies to:
[tex]\[ x = -4 \][/tex]
So, the solution to the equation [tex]\( -4(x - 2) + 2x = 16 \)[/tex] is:
[tex]\[ x = -4 \][/tex]
