If $L M ∥ A B, A L = x - 3, A C = 2 x, B M = x - 2,$ and $B C = 2 x + 3.$ What is value of $A C ?$

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Solution

Given, $L M ∥ A B,$
So, $\frac{C L}{C A} = \frac{C M}{C B}$
$\Rightarrow \frac{(x - 3)}{2 x} = \frac{(x - 2)}{(2 x + 3)}$
$\Rightarrow x = 9$
So, $A C = 2 x = 18$

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