Question

practice set #2: use segment addition to answer the following. 3. label the picture and find the missing segment. fy = 29 fl = 3x - 9 ly = 4x + 3 find x. find fl.

Explanation:

Step1: Apply segment - addition postulate

By the segment - addition postulate, $FY=FL + LY$. Substitute the given expressions: $29=(3x - 9)+(4x + 3)$.

Step2: Simplify the right - hand side

Combine like terms: $29 = 3x-9 + 4x+3=7x-6$.

Step3: Solve for x

Add 6 to both sides of the equation: $29 + 6=7x-6 + 6$, which gives $35 = 7x$. Then divide both sides by 7: $x=\frac{35}{7}=5$.

Step4: Find FL

Substitute $x = 5$ into the expression for $FL$. $FL=3x - 9$. So $FL=3\times5-9=15 - 9 = 6$.

Answer:

$x = 5$
$FL = 6$