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

Since $KL+LM = KM$, we have $2x + 3x=7x - 8$.

Step2: Simplify the left - hand side

$2x+3x = 5x$, so the equation becomes $5x=7x - 8$.

Step3: Isolate the variable

Subtract $5x$ from both sides: $0 = 7x-5x - 8$, which simplifies to $0 = 2x - 8$. Then add 8 to both sides: $8 = 2x$.

Step4: Solve for x

Divide both sides by 2: $x=\frac{8}{2}=4$.

Step5: Find the length of LM

Substitute $x = 4$ into the expression for $LM$. $LM = 3x$, so $LM=3\times4 = 12$.

Step6: Find the length of KL

Substitute $x = 4$ into the expression for $KL$. $KL = 2x$, so $KL=2\times4 = 8$.

Step7: Find the length of KM

Substitute $x = 4$ into the expression for $KM$. $KM = 7x - 8$, so $KM=7\times4 - 8=28 - 8=20$.

Answer:

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