Question

13 multiple choice 1 point
what is the solution of $\frac{3}{x-2}+6=\frac{15}{x-2}$ ?
10
20
4
6
clear my selection
previous

Explanation:

Step1: Eliminate denominator

Multiply all terms by $x-2$ (where $x
eq 2$):
$$3 + 6(x-2) = 15$$

Step2: Expand the left side

$$3 + 6x - 12 = 15$$

Step3: Simplify left side

Combine constant terms:
$$6x - 9 = 15$$

Step4: Isolate variable term

Add 9 to both sides:
$$6x = 15 + 9$$
$$6x = 24$$

Step5: Solve for x

Divide by 6:
$$x = \frac{24}{6} = 4$$

Step6: Verify solution

Substitute $x=4$ into original equation:
$$\frac{3}{4-2} + 6 = \frac{15}{4-2}$$
$$\frac{3}{2} + 6 = \frac{15}{2}$$
$$\frac{3}{2} + \frac{12}{2} = \frac{15}{2}$$
$$\frac{15}{2} = \frac{15}{2}$$
The solution is valid.

Answer:

4