We are given the equation:
>
$\frac{2}{3}(9x - 6) - 4 = 9x - 6$
And we are asked to find the value of
$3x - 2$.
---
Step 1: Simplify the left-hand side (LHS)
Distribute $\frac{2}{3}$ into $(9x - 6)$:
$$
\frac{2}{3} \cdot 9x = 6x, \quad \frac{2}{3} \cdot (-6) = -4
$$
So,
$$
\text{LHS} = 6x - 4 - 4 = 6x - 8
$$
Now the equation becomes:
$$
6x - 8 = 9x - 6
$$
---
Step 2: Solve for $x$
Subtract $6x$ from both sides:
$$
-8 = 3x - 6
$$
Add 6 to both sides:
$$
-2 = 3x
$$
Divide by 3:
$$
x = -\frac{2}{3}
$$
---
Step 3: Find $3x - 2$
Plug in $x = -\frac{2}{3}$:
$$
3x - 2 = 3 \cdot \left(-\frac{2}{3}\right) - 2 = -2 - 2 = -4
$$
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✔ Final Answer: A) $-4$
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Parent Tip: Review the logic above to help your child master the concept of sat math worksheet.
