Question

section 1.2 i can use the segment addition postulate. 6. point l is on the line segment km. given km = 7x - 8, lm = 3x, and kl = 2x, find the value of x and the measures of each segment.

Explanation:

Step1: Apply segment - addition postulate

$KL+LM = KM$

Step2: Substitute given expressions

$2x + 3x=7x - 8$

Step3: Combine like - terms on left side

$5x=7x - 8$

Step4: Move terms with $x$ to one side

$7x-5x = 8$

Step5: Simplify

$2x=8$

Step6: Solve for $x$

$x = 4$

Step7: Find length of $LM$

$LM = 3x=3\times4 = 12$

Step8: Find length of $KL$

$KL=2x=2\times4 = 8$

Step9: Find length of $KM$

$KM=7x - 8=7\times4-8=28 - 8=20$

Answer:

$x = 4$
$LM=12$
$KL = 8$
$KM=20$