## Intermediate Algebra: Connecting Concepts through Application

$13$
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: $13$.
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