Answer
$13$
Work Step by Step
Multiply $x-7$ to both sides of the equation to obtain:
$4(x-7) = \dfrac{24}{x-7} \cdot (x-7)
\\4(x)-4(7)=24
\\4x-28=24$
Add $28$ to both sides of the equation to obtain:
$4x=24+28
\\4x=52$
Divide $4$ to both sides to obtain:
$x = \frac{52}{4}
\\x=13$
Cheking:
$4=\dfrac{24}{13-7}?
\\4 = \dfrac{24}{6}?
\\4=4$
Thus, the solution to the given equation is: $13$.