Let's solve the equation step by step:
Given equation:
[tex]\[
-(2x - 3) - (4x - 6) + 4 = -4(x - 1) - (5x + 3) + 3
\][/tex]
Step 1: Simplify the left side of the equation
[tex]\[
-(2x - 3) - (4x - 6) + 4
\][/tex]
First, distribute the negative sign:
[tex]\[
-2x + 3 - 4x + 6 + 4
\][/tex]
Combine like terms:
[tex]\[
-2x - 4x + 3 + 6 + 4 = -6x + 13
\][/tex]
Step 2: Simplify the right side of the equation
[tex]\[
-4(x - 1) - (5x + 3) + 3
\][/tex]
Distribute the negative signs:
[tex]\[
-4x + 4 - 5x - 3 + 3
\][/tex]
Combine like terms:
[tex]\[
-4x - 5x + 4 - 3 + 3 = -9x + 4
\][/tex]
Now, our simplified equation is:
[tex]\[
-6x + 13 = -9x + 4
\][/tex]
Step 3: Solve for [tex]\(x\)[/tex]
Start by getting all [tex]\(x\)[/tex]-terms on one side of the equation. Add [tex]\(9x\)[/tex] to both sides:
[tex]\[
-6x + 9x + 13 = 4
\][/tex]
Combine like terms:
[tex]\[
3x + 13 = 4
\][/tex]
Next, isolate the [tex]\(x\)[/tex]-term by subtracting 13 from both sides:
[tex]\[
3x = 4 - 13
\][/tex]
[tex]\[
3x = -9
\][/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{-9}{3}
\][/tex]
[tex]\[
x = -3
\][/tex]
So, the solution is:
[tex]\[
\boxed{-3}
\][/tex]
