Certainly! Let's go through each step of solving the equation in detail:
1. Given Equation:
[tex]\[
-6 = -\frac{2}{3}(x + 12) + \frac{1}{3}x
\][/tex]
This is the given equation we need to solve.
2. Distribute the [tex]\(-\frac{2}{3}\)[/tex] to the terms inside the parenthesis:
[tex]\[
-6 = -\frac{2}{3}x - \frac{2}{3} \times 12 + \frac{1}{3}x
\][/tex]
Simplify the multiplication inside the parenthesis:
[tex]\[
-6 = -\frac{2}{3}x - 8 + \frac{1}{3}x
\][/tex]
3. Combine like terms:
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
-\frac{2}{3}x + \frac{1}{3}x = -\frac{1}{3}x
\][/tex]
So, we have:
[tex]\[
-6 = -\frac{1}{3}x - 8
\][/tex]
4. Add 8 to both sides (Addition property of equality):
[tex]\[
-6 + 8 = -\frac{1}{3}x
\][/tex]
Simplify the left side:
[tex]\[
2 = -\frac{1}{3}x
\][/tex]
5. Multiply both sides by [tex]\(-3\)[/tex] (Multiplication property of equality):
[tex]\[
2 \times -3 = x
\][/tex]
Simplify the multiplication:
[tex]\[
-6 = x
\][/tex]
6. Symmetric property:
Using the symmetric property of equality, we write the final result:
[tex]\[
x = -6
\][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = -6 \][/tex]
