Certainly! Let's solve the equation step-by-step: [tex]\( -(3x - 2) = -4(x + 1) - 4 \)[/tex].
1. Distribute through the parentheses:
[tex]\[-(3x - 2) = -4(x + 1) - 4\][/tex]
Applying the negative sign to the terms inside the parentheses on the left:
[tex]\[-3x + 2 = -4(x + 1) - 4\][/tex]
2. Distribute [tex]\(-4\)[/tex] on the right side:
[tex]\[-3x + 2 = -4x - 4 - 4\][/tex]
Simplify the right side:
[tex]\[-3x + 2 = -4x - 8\][/tex]
3. Isolate [tex]\(x\)[/tex]:
Add [tex]\(4x\)[/tex] to both sides to get all terms involving [tex]\(x\)[/tex] on one side:
[tex]\[-3x + 4x + 2 = -4x + 4x - 8\][/tex]
Simplify:
[tex]\(x + 2 = -8\)[/tex]
4. Solve for [tex]\(x\)[/tex]:
Subtract 2 from both sides:
[tex]\(x + 2 - 2 = -8 - 2\)[/tex]
Simplify:
[tex]\(x = -10\)[/tex]
Therefore, the solution to the equation [tex]\( -(3x - 2) = -4(x + 1) - 4 \)[/tex] is [tex]\( x = -10 \)[/tex].
Given the options:
- [tex]\(-2\)[/tex]
- [tex]\(-10\)[/tex]
- [tex]\(2\)[/tex]
- [tex]\(10\)[/tex]
The correct answer is [tex]\(-10\)[/tex].
