Question

Solve and check the following linear equation.
6 x minus left parenthesis 3 x minus 9 right parenthesis equals 36

Answer 1

To solve the equation \( 6x - (3x - 9) = 36 \), we begin by simplifying the left side of the equation.

1. Distribute the negative sign:
\[
6x - 3x + 9 = 36
\]

2. Combine like terms:
\[
(6x - 3x) + 9 = 36
\]
\[
3x + 9 = 36
\]

3. Next, isolate the variable \( x \) by subtracting 9 from both sides:
\[
3x + 9 - 9 = 36 - 9
\]
\[
3x = 27
\]

4. Now, divide both sides by 3 to solve for \( x \):
\[
x = \frac{27}{3}
\]
\[
x = 9
\]

Now that we have found \( x = 9 \), we will check the solution by substituting \( x \) back into the original equation.

### Check:
Substitute \( x = 9 \) into the original equation:
\[
6(9) - (3(9) - 9) = 36
\]
Calculate the left side:
\[
54 - (27 - 9) = 36
\]
Simplifying inside the parentheses:
\[
54 - 18 = 36
\]
Now calculate:
\[
36 = 36
\]

Since both sides of the equation are equal, our solution is confirmed to be correct.

Thus, the final solution is:
\[
\boxed{9}
\]