To solve the equation [tex]\(-4(6x + 3) = -12(x + 10)\)[/tex] step-by-step, we need to follow the process of distributing, simplifying, and isolating the variable [tex]\(x\)[/tex]. Here is the detailed solution:
1. Distribute the constants on both sides of the equation:
On the left side, distribute [tex]\(-4\)[/tex] over the terms inside the parentheses:
[tex]\[
-4(6x + 3) = -4 \cdot 6x + (-4) \cdot 3 = -24x - 12
\][/tex]
On the right side, distribute [tex]\(-12\)[/tex] over the terms inside the parentheses:
[tex]\[
-12(x + 10) = -12 \cdot x + (-12) \cdot 10 = -12x - 120
\][/tex]
2. Rewrite the equation with the distributed terms:
[tex]\[
-24x - 12 = -12x - 120
\][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
To do this, add [tex]\(24x\)[/tex] to both sides of the equation to move the [tex]\(x\)[/tex] terms together:
[tex]\[
-24x + 24x - 12 = -12x + 24x - 120
\][/tex]
Simplifying gives:
[tex]\[
-12 = 12x - 120
\][/tex]
4. Move the constant terms to the other side of the equation:
Add 120 to both sides of the equation to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-12 + 120 = 12x - 120 + 120
\][/tex]
Simplifying gives:
[tex]\[
108 = 12x
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by 12:
[tex]\[
\frac{108}{12} = \frac{12x}{12}
\][/tex]
Simplifying gives:
[tex]\[
9 = x
\][/tex]
So, the solution to the equation [tex]\(-4(6x + 3) = -12(x + 10)\)[/tex] is [tex]\(x = 9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{9} \][/tex]
