Question

what value of x would make km || jn?
complete the statements to solve for x.
by the converse of the side - splitter theorem, if jk/kl =
◻, then km || jn.
substitute the expressions into the proportion:
(x - 5)/x = (x - 3)/(x + 4).
cross - multiply: (x - 5)(◻) = x(x - 3).
distribute: x(x)+x(4)-5(x)-5(4)=x(x)+x(-3).
multiply and simplify: x² - x - ◻ = x² - 3x.
solve for x: x = ◻.

Explanation:

Step1: Cross - multiply

$$(x - 5)(x - 3)=x(x + 4)$$

Step2: Distribute

$$x(x)-x(3)-5(x)+5(3)=x(x)+x(4)$$
$$x^{2}-3x-5x + 15=x^{2}+4x$$

Step3: Simplify

$$x^{2}-8x + 15=x^{2}+4x$$
Subtract \(x^{2}\) from both sides:
$$-8x + 15=4x$$
Add \(8x\) to both sides:
$$15 = 12x$$

Step4: Solve for \(x\)

Divide both sides by \(12\):
$$x=\frac{15}{12}=\frac{5}{4}=1.25$$

Answer:

\(x = 1.25\)