Exercise 14 Page 582

Let's analyze the given figure.

Since we are given three parallel lines that intersect two transversals, we can use the Corollary to the Triangle Proportionality Theorem.

The lengths of the segments intercepted on the transversals are proportional. Let's write a proportion using the expressions for the lengths of the segments. 17+5y/13+6y=3x-9/4x-22 Notice that XY=YZ, thus we can solve the equation 3x-9 = 4x-22 to find x.

3x-9 = 4x-22

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Solve for x

AddEqn

LHS+22=RHS+22

3x+13=4x

SubEqn

LHS-3x=RHS-3x

13=x

RearrangeEqn

Rearrange equation

x=13