Sure! Let’s go through the solution step-by-step.
1. Given Equation:
[tex]\[ 2(4x + 2) = 4x - 12(x - 1) \][/tex]
2. Simplify both sides:
- Left Side:
[tex]\[ 2(4x + 2) \][/tex]
Distribute the 2:
[tex]\[ 2 \cdot 4x + 2 \cdot 2 \][/tex]
[tex]\[ 8x + 4 \][/tex]
- Right Side:
[tex]\[ 4x - 12(x - 1) \][/tex]
Distribute the -12:
[tex]\[ 4x - 12 \cdot x - 12 \cdot (-1) \][/tex]
Combine like terms:
[tex]\[ 4x - 12x + 12 \][/tex]
Simplify:
[tex]\[ -8x + 12 \][/tex]
3. Rewrite the simplified equation:
[tex]\[ 8x + 4 = -8x + 12 \][/tex]
4. Move terms involving [tex]\(x\)[/tex] to one side and constants to the other side:
[tex]\[ 8x + 8x + 4 = 12 \][/tex]
Combine like terms:
[tex]\[ 16x + 4 = 12 \][/tex]
5. Isolate term with [tex]\(x\)[/tex]:
Subtract 4 from both sides:
[tex]\[ 16x = 12 - 4 \][/tex]
[tex]\[ 16x = 8 \][/tex]
6. Solve for [tex]\(x\)[/tex]:
Divide both sides by 16:
[tex]\[ x = \frac{8}{16} \][/tex]
Simplify the fraction:
[tex]\[ x = 0.5 \][/tex]
So, the solution to the equation [tex]\(2(4x + 2) = 4x - 12(x - 1)\)[/tex] is:
[tex]\[ x = 0.5 \][/tex]
