Question

question point j is on line segment $overline{ik}$. given $jk = 2x - 1$, $ik = 3x + 2$, and $ij = 3x - 5$, determine the numerical length of $overline{jk}$. answer attempt 1 out of 2 $jk =$

Explanation:

Step1: Use segment - addition postulate

Since point $J$ is on line segment $\overline{IK}$, we have $IJ + JK=IK$. Substitute the given expressions: $(3x - 5)+(2x - 1)=3x + 2$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+2x-5 - 1=3x + 2$, which simplifies to $5x-6 = 3x+2$.

Step3: Solve for $x$

Subtract $3x$ from both sides: $5x-3x-6=3x - 3x+2$, so $2x-6 = 2$. Then add 6 to both sides: $2x-6 + 6=2 + 6$, giving $2x=8$. Divide both sides by 2: $x = 4$.

Step4: Find the length of $JK$

Substitute $x = 4$ into the expression for $JK$. Since $JK=2x - 1$, then $JK=2\times4-1$. Calculate $2\times4-1=8 - 1=7$.

Answer:

$7$