Question

if k is the midpoint of $overline{er}$, $ek = 3x + 7$, and $rk = 5x - 9$, what is the length of segment $er$? draw and label a diagram, along with showing your solving. $x=square$ $er=square$

Explanation:

Step1: Set up equation using mid - point property

Since K is the mid - point of $\overline{ER}$, then $EK = RK$. So we set up the equation $3x + 7=5x - 9$.

Step2: Solve for x

Subtract $3x$ from both sides: $7 = 5x-3x - 9$, which simplifies to $7 = 2x-9$. Then add 9 to both sides: $7 + 9=2x$, so $16 = 2x$. Divide both sides by 2, we get $x = 8$.

Step3: Find the length of $EK$ or $RK$

Substitute $x = 8$ into the expression for $EK$ (we could also use $RK$). $EK=3x + 7=3\times8 + 7=24 + 7=31$.

Step4: Find the length of $ER$

Since $ER=EK + RK$ and $EK = RK$, then $ER = 2\times EK$. So $ER=2\times31 = 62$.

Answer:

$x = 8$
$ER = 62$