To solve the equation [tex]\(-10 - 4(8 + 6x) = -2(2x + 1)\)[/tex], let's follow these steps:
1. Distribute the constants inside the parentheses:
[tex]\[
-10 - 4(8 + 6x) = -2(2x + 1)
\][/tex]
[tex]\[
-10 - (4 \cdot 8) - (4 \cdot 6x) = -2(2x) - 2(1)
\][/tex]
Simplify each term:
[tex]\[
-10 - 32 - 24x = -4x - 2
\][/tex]
2. Combine like terms on each side:
On the left side:
[tex]\[
-10 - 32 - 24x = -42 - 24x
\][/tex]
So, the equation now looks like:
[tex]\[
-42 - 24x = -4x - 2
\][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side:
Add [tex]\(24x\)[/tex] to both sides:
[tex]\[
-42 - 24x + 24x = -4x + 24x - 2
\][/tex]
Simplify:
[tex]\[
-42 = 20x - 2
\][/tex]
Add 2 to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-42 + 2 = 20x - 2 + 2
\][/tex]
[tex]\[
-40 = 20x
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 20:
[tex]\[
x = \frac{-40}{20}
\][/tex]
Simplify:
[tex]\[
x = -2
\][/tex]
Therefore, the solution to the equation [tex]\(-10 - 4(8 + 6x) = -2(2x + 1)\)[/tex] is:
[tex]\[
x = -2
\][/tex]
