Question

problem 16: (first taught in lesson 12) if line (l) bisects (overline{kp}) at point (l), and if (kl = 7x + 1) and (lp = 8x - 3), find (kp). after you enter your answer press go. (kp=)

Explanation:

Step1: Set KL equal to LP

Since line $\ell$ bisects $\overline{KP}$ at point $L$, then $KL = LP$. So, $7x + 1=8x - 3$.

Step2: Solve for x

Subtract $7x$ from both sides: $1=x - 3$. Then add 3 to both sides, we get $x = 4$.

Step3: Find KL or LP

Substitute $x = 4$ into the expression for $KL$: $KL=7x + 1=7\times4+1=29$. (We could also use the expression for $LP$: $LP = 8x - 3=8\times4-3 = 29$).

Step4: Calculate KP

Since $KP=KL + LP$ and $KL = LP = 29$, then $KP=29+29 = 46$.

Answer:

46