Question

question point i is on line segment $overline{hj}$. given $ij = 3x + 3, hi = 3x - 1$, and $hj = 3x + 8$, determine the numerical length of $overline{hj}$. answer attempt 1 out of 2 $hj=$

Explanation:

Step1: Use segment - addition postulate

Since point $I$ is on line segment $\overline{HJ}$, we know that $HI + IJ=HJ$. Substitute the given expressions: $(3x - 1)+(3x + 3)=3x + 8$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x-1 + 3x+3=(3x + 3x)+(-1 + 3)=6x+2$. So, $6x + 2=3x + 8$.

Step3: Solve for $x$

Subtract $3x$ from both sides: $6x-3x + 2=3x-3x + 8$, which gives $3x+2 = 8$. Then subtract 2 from both sides: $3x+2-2=8 - 2$, so $3x=6$. Divide both sides by 3: $x = 2$.

Step4: Find the length of $HJ$

Substitute $x = 2$ into the expression for $HJ$. Since $HJ=3x + 8$, then $HJ=3\times2+8=6 + 8=14$.

Answer:

$14$