Certainly! Let's solve the equation step by step:
Given equation:
[tex]\[
3(x + 2) = 2(2 - x)
\][/tex]
1. Distribute the coefficients to the terms inside the parentheses:
[tex]\[
3 \cdot (x + 2) = 3x + 6
\][/tex]
[tex]\[
2 \cdot (2 - x) = 4 - 2x
\][/tex]
So, the equation becomes:
[tex]\[
3x + 6 = 4 - 2x
\][/tex]
2. Move all the terms involving [tex]\( x \)[/tex] to one side of the equation and the constant terms to the other side to solve for [tex]\( x \)[/tex]:
[tex]\[
3x + 6 + 2x = 4 - 2x + 2x
\][/tex]
Simplify both sides:
[tex]\[
5x + 6 = 4
\][/tex]
3. Isolate the term with [tex]\( x \)[/tex] by subtracting 6 from both sides:
[tex]\[
5x = 4 - 6
\][/tex]
Simplify the right-hand side:
[tex]\[
5x = -2
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[
x = \frac{-2}{5}
\][/tex]
Therefore, the solution is:
[tex]\[
x = -\frac{2}{5}
\][/tex]
Hence, the correct answer is:
B. [tex]\( x = -\frac{2}{5} \)[/tex]
