Question

09/03 - segment bisector practice l (updated)
line l bisects each segment. set up an equation to find x and then find the specified lengths.
x 28 t 5x + 3 w
equation: = (no spaces)
x = xt = tw = xw =

Explanation:

Step1: Use bisection property

Since line $l$ bisects segment $XW$, we have $XT = TW$. So the equation is $28=5x + 3$.

Step2: Solve for $x$

Subtract 3 from both sides of the equation: $28 - 3=5x+3 - 3$, which simplifies to $25 = 5x$. Then divide both sides by 5: $x=\frac{25}{5}=5$.

Step3: Find $XT$

We know $XT = 28$.

Step4: Find $TW$

Since $TW=5x + 3$ and $x = 5$, then $TW=5\times5+3=25 + 3=28$.

Step5: Find $XW$

$XW=XT + TW$, so $XW=28+28 = 56$.

Answer:

Equation: $28=5x + 3$
$x = 5$
$XT = 28$
$TW = 28$
$XW = 56$