Question

What value will complete the set of equations 15/3x−9
− 4 = 12
and x≠
_____?(1 point)
The value that completes the set of equations is x≠
.

Answer 1

To solve the equation \( \frac{15}{3x - 9} - 4 = 12 \), we first isolate \( \frac{15}{3x - 9} \).

1. Add 4 to both sides of the equation:
\[
\frac{15}{3x - 9} = 12 + 4
\]
\[
\frac{15}{3x - 9} = 16
\]

2. Now, multiply both sides by \( (3x - 9) \) to eliminate the fraction (assuming \( 3x - 9 \neq 0 \)):
\[
15 = 16(3x - 9)
\]

3. Distributing on the right side gives:
\[
15 = 48x - 144
\]

4. Next, add 144 to both sides:
\[
15 + 144 = 48x
\]
\[
159 = 48x
\]

5. Divide both sides by 48 to solve for \( x \):
\[
x = \frac{159}{48}
\]

Now, we need to determine when \( 3x - 9 \neq 0 \) to find the value that \( x \) cannot equal:

1. Set \( 3x - 9 = 0 \):
\[
3x = 9
\]
\[
x = 3
\]

So, the value that completes the set of equations is \( x \neq 3 \).

Therefore, the final answer is:
\[
x \neq 3
\]