To solve the equation [tex]\(3(x + 1) = 2(x - 1)\)[/tex], let's go through the steps to isolate and solve for [tex]\(x\)[/tex].
1. Begin by distributing the constants on both sides of the equation:
[tex]\[
3(x + 1) = 3 \cdot x + 3 \cdot 1 = 3x + 3
\][/tex]
[tex]\[
2(x - 1) = 2 \cdot x - 2 \cdot 1 = 2x - 2
\][/tex]
2. Now, the equation looks like this:
[tex]\[
3x + 3 = 2x - 2
\][/tex]
3. To isolate [tex]\(x\)[/tex], we need to get all terms involving [tex]\(x\)[/tex] on one side of the equation and the constant terms on the other side. First, subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
3x - 2x + 3 = -2
\][/tex]
[tex]\[
x + 3 = -2
\][/tex]
4. Next, subtract 3 from both sides to solve for [tex]\(x\)[/tex]:
[tex]\[
x + 3 - 3 = -2 - 3
\][/tex]
[tex]\[
x = -5
\][/tex]
So, the solution for [tex]\(x\)[/tex] is [tex]\(-5\)[/tex].
Among the given choices:
[tex]\[
-5, -4, -2, -1
\][/tex]
The correct answer is [tex]\(-5\)[/tex].
