Sure! Let's solve the equation step by step:
We start with the given equation:
[tex]\[ 4x - 8 = -4(2x - 3) + 4 \][/tex]
1. Distribute the [tex]\(-4\)[/tex] on the right side of the equation:
[tex]\[ -4(2x - 3) = -4 \cdot 2x + (-4 \cdot -3) \][/tex]
[tex]\[ -4(2x - 3) = -8x + 12 \][/tex]
2. Substitute [tex]\(-8x + 12\)[/tex] back into our equation:
[tex]\[ 4x - 8 = -8x + 12 + 4 \][/tex]
3. Combine like terms on the right side:
[tex]\[ 4x - 8 = -8x + 16 \][/tex]
4. Add [tex]\(8x\)[/tex] to both sides to start isolating [tex]\(x\)[/tex]:
[tex]\[ 4x + 8x - 8 = 16 \][/tex]
[tex]\[ 12x - 8 = 16 \][/tex]
5. Add [tex]\(8\)[/tex] to both sides to further isolate [tex]\(x\)[/tex]:
[tex]\[ 12x - 8 + 8 = 16 + 8 \][/tex]
[tex]\[ 12x = 24 \][/tex]
6. Finally, divide both sides by [tex]\(12\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{24}{12} \][/tex]
[tex]\[ x = 2 \][/tex]
The solution to the equation [tex]\( 4x - 8 = -4(2x - 3) + 4 \)[/tex] is [tex]\( x = 2 \)[/tex].
