What value will complete the set of equations 15/

Question

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 the fraction:

1. Add 4 to both sides: $$\frac{15}{3x-9}=12+4$$ $$\frac{15}{3x-9}=16$$

2. Now, cross-multiply to eliminate the fraction: $$15=16(3x-9)$$

3. Distribute the 16: $$15=48x-144$$

4. Rearranging gives: $$48x=15+144$$ $$48x=159$$

5. Now, solve for $x$: $$x=\frac{159}{48}$$

Next, we must determine any restrictions on $x$. The original equation contains a fraction, which means the denominator cannot be zero. Set the denominator equal to zero and solve for $x$: $$3x-9=0$$ $$3x=9$$ $$x=3$$

Thus, the value that completes the set of equations is $x\ne 3$.

So the final answer is: $$\text{The value that completes the set of equations is }x\ne 3.$$