Question

if de = 4x - 1, ef = 9, and df = 9x - 22, find the value of x.

Explanation:

Step1: Use segment - addition postulate

Since $DF=DE + EF$, we substitute the given expressions: $9x - 22=(4x - 1)+9$.

Step2: Simplify the right - hand side

$(4x - 1)+9=4x+(-1 + 9)=4x + 8$. So the equation becomes $9x - 22=4x + 8$.

Step3: Subtract 4x from both sides

$9x-4x - 22=4x-4x + 8$, which simplifies to $5x-22 = 8$.

Step4: Add 22 to both sides

$5x-22 + 22=8 + 22$, resulting in $5x=30$.

Step5: Divide both sides by 5

$\frac{5x}{5}=\frac{30}{5}$, so $x = 6$.

Answer:

6