Certainly! Let's solve the equation step-by-step.
Given equation:
[tex]\[ 2(3x + 4) + 2 = 4 + 3x \][/tex]
1. Distribute the 2 on the left-hand side:
[tex]\[ 2 \cdot (3x + 4) + 2 = 2 \cdot 3x + 2 \cdot 4 + 2 \][/tex]
[tex]\[ 2 \cdot 3x = 6x \][/tex]
[tex]\[ 2 \cdot 4 = 8 \][/tex]
So, we have:
[tex]\[ 6x + 8 + 2 \][/tex]
2. Simplify the left side:
[tex]\[ 6x + 8 + 2 = 6x + 10 \][/tex]
Now the equation is:
[tex]\[ 6x + 10 = 4 + 3x \][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side and constants to the other side:
Subtract [tex]\(3x\)[/tex] from both sides:
[tex]\[ 6x + 10 - 3x = 4 + 3x - 3x \][/tex]
[tex]\[ 3x + 10 = 4 \][/tex]
4. Move constant terms to the other side:
Subtract 10 from both sides:
[tex]\[ 3x + 10 - 10 = 4 - 10 \][/tex]
[tex]\[ 3x = -6 \][/tex]
5. Solve for [tex]\(x\)[/tex]:
Divide both sides by 3:
[tex]\[ x = \frac{-6}{3} \][/tex]
[tex]\[ x = -2 \][/tex]
Therefore, the solution is:
[tex]\[ x = -2 \][/tex]
