Certainly! Let's solve the equation [tex]\(-4(x-8)-6=-5(x+3)\)[/tex] step by step.
1. Distribute the multiplication on both sides:
On the left side, distribute [tex]\(-4\)[/tex] into [tex]\((x - 8)\)[/tex]:
[tex]\[
-4(x - 8) = -4x + 32
\][/tex]
With the [tex]\(-6\)[/tex] still present, we have:
[tex]\[
-4x + 32 - 6
\][/tex]
Simplify:
[tex]\[
-4x + 26
\][/tex]
On the right side, distribute [tex]\(-5\)[/tex] into [tex]\((x + 3)\)[/tex]:
[tex]\[
-5(x + 3) = -5x - 15
\][/tex]
2. Write the equation with the simplified expressions:
[tex]\[
-4x + 26 = -5x - 15
\][/tex]
3. Collect all [tex]\(x\)[/tex]-terms on one side:
Add [tex]\(5x\)[/tex] to both sides to move the [tex]\(x\)[/tex] terms to one side:
[tex]\[
-4x + 26 + 5x = -5x - 15 + 5x
\][/tex]
Simplify:
[tex]\[
x + 26 = -15
\][/tex]
4. Isolate [tex]\(x\)[/tex]:
Subtract 26 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x + 26 - 26 = -15 - 26
\][/tex]
Simplify:
[tex]\[
x = -41
\][/tex]
The solution to the equation [tex]\(-4(x-8)-6=-5(x+3)\)[/tex] is [tex]\(x = -41\)[/tex].
