Sure, let's solve the equation step by step.
Given:
[tex]\[
\frac{3(8x + 24)}{12} = 9 - 3(x - 4)
\][/tex]
Step 1: Simplify the left side of the equation
First, distribute the 3 inside the parentheses:
[tex]\[
3(8x + 24) = 3 \cdot 8x + 3 \cdot 24 = 24x + 72
\][/tex]
Then, divide by 12:
[tex]\[
\frac{24x + 72}{12} = \frac{24x}{12} + \frac{72}{12} = 2x + 6
\][/tex]
So, the left side of the equation simplifies to:
[tex]\[
2x + 6
\][/tex]
Step 2: Simplify the right side of the equation
First, distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[
-3(x - 4) = -3x + 12
\][/tex]
Then add the 9:
[tex]\[
9 - 3x + 12 = -3x + 21
\][/tex]
So, the right side of the equation simplifies to:
[tex]\[
-3x + 21
\][/tex]
Step 3: Combine the simplified expressions
Now the equation is:
[tex]\[
2x + 6 = -3x + 21
\][/tex]
Step 4: Combine like terms
Add [tex]\(3x\)[/tex] to both sides to get all [tex]\(x\)[/tex]-terms on one side:
[tex]\[
2x + 3x + 6 = 21
\][/tex]
[tex]\[
5x + 6 = 21
\][/tex]
Subtract 6 from both sides to isolate the [tex]\(x\)[/tex]-term:
[tex]\[
5x = 21 - 6
\][/tex]
[tex]\[
5x = 15
\][/tex]
Step 5: Solve for [tex]\(x\)[/tex]
Finally, divide by 5:
[tex]\[
x = \frac{15}{5}
\][/tex]
[tex]\[
x = 3
\][/tex]
So, the solution is:
[tex]\[
x = 3
\][/tex]
