Let's start by simplifying both sides of the equation step by step.
Given the equation:
[tex]\[
-2(3x + 3) = 8 - 5(4 - 2x)
\][/tex]
First, distribute the constants through the parentheses.
For the left side:
[tex]\[
-2(3x + 3) = -2 \cdot 3x + (-2) \cdot 3 = -6x - 6
\][/tex]
For the right side:
[tex]\[
8 - 5(4 - 2x) = 8 - 5 \cdot 4 + 5 \cdot 2x = 8 - 20 + 10x
\][/tex]
Combine like terms on the right side:
[tex]\[
8 - 20 + 10x = -12 + 10x
\][/tex]
Now the equation is:
[tex]\[
-6x - 6 = -12 + 10x
\][/tex]
To solve for [tex]\( x \)[/tex], isolate the terms involving [tex]\( x \)[/tex] on one side of the equation and the constants on the other.
Add [tex]\( 6x \)[/tex] to both sides:
[tex]\[
-6x - 6 + 6x = -12 + 10x + 6x \][/tex]
[tex]\[
-6 = -12 + 16x
\][/tex]
Add 12 to both sides:
[tex]\[
-6 + 12 = -12 + 12 + 16x
\][/tex]
[tex]\[
6 = 16x
\][/tex]
Finally, divide both sides by 16:
[tex]\[
\frac{6}{16} = x
\][/tex]
[tex]\[
x = \frac{6}{16}
\][/tex]
Simplify the fraction:
[tex]\[
x = \frac{3}{8}
\][/tex]
So, the equivalent equation of the form [tex]\( ax = b \)[/tex] is:
[tex]\[
16x = 6
\][/tex]
Thus, the equivalent equation is:
[tex]\[
16x = 6
\][/tex]
The correct answer is:
[tex]\[
\boxed{16x = 6}
\][/tex]
