Problem:
We are given the equation:
\[
\frac{2}{3}(9x - 6) - 4 = 9x - 6
\]
and we need to find the value of \(3x - 2\).
Step-by-Step Solution:
1.
Simplify the left-hand side of the equation:
\[
\frac{2}{3}(9x - 6) - 4
\]
Distribute \(\frac{2}{3}\) across the terms inside the parentheses:
\[
\frac{2}{3} \cdot 9x - \frac{2}{3} \cdot 6 = 6x - 4
\]
So the left-hand side becomes:
\[
6x - 4 - 4 = 6x - 8
\]
2.
Rewrite the equation:
Substitute the simplified left-hand side back into the equation:
\[
6x - 8 = 9x - 6
\]
3.
Isolate \(x\):
To isolate \(x\), first move all terms involving \(x\) to one side and constant terms to the other side. Subtract \(6x\) from both sides:
\[
6x - 8 - 6x = 9x - 6 - 6x
\]
Simplify:
\[
-8 = 3x - 6
\]
Next, add 6 to both sides to isolate the term with \(x\):
\[
-8 + 6 = 3x - 6 + 6
\]
Simplify:
\[
-2 = 3x
\]
4.
Solve for \(x\):
Divide both sides by 3:
\[
x = \frac{-2}{3}
\]
5.
Find the value of \(3x - 2\):
Substitute \(x = \frac{-2}{3}\) into the expression \(3x - 2\):
\[
3x - 2 = 3 \left( \frac{-2}{3} \right) - 2
\]
Simplify:
\[
3 \left( \frac{-2}{3} \right) = -2
\]
So:
\[
3x - 2 = -2 - 2 = -4
\]
Final Answer:
\[
\boxed{-4}
\]
Thus, the correct option is \(\boxed{\text{A}}\).
Parent Tip: Review the logic above to help your child master the concept of free sat math worksheet.
