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

Let's solve the equation step by step:

Given the equation:

\[
\frac{15}{3x - 9} - 4 = 12
\]

First, we can isolate the fraction by adding 4 to both sides:

\[
\frac{15}{3x - 9} = 12 + 4
\]
\[
\frac{15}{3x - 9} = 16
\]

Next, we can eliminate the fraction by cross-multiplying or multiplying both sides by \(3x - 9\):

\[
15 = 16(3x - 9)
\]

Distributing on the right side:

\[
15 = 48x - 144
\]

Next, we can solve for \(x\) by adding 144 to both sides:

\[
15 + 144 = 48x
\]
\[
159 = 48x
\]

Now, divide both sides by 48:

\[
x = \frac{159}{48}
\]

Next, we need to check the restrictions on \(x\). The denominator \(3x - 9\) must not equal zero:

\[
3x - 9 \neq 0
\]
\[
3x \neq 9
\]
\[
x \neq 3
\]

Thus, the value that completes the set of equations is:

\[
x \neq 3
\]

So, the answer is:

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