Question

ch. 1.2 - segment addition postulate
possible points: 10
if u is between t and b, find the value of x and the lengths of the segments. (hint: draw a picture for each problem with the given information and then write the equation to solve.)
tu = 4x - 1, ub = 2x - 1, tb = 5x
x =
tu =
ub =
tb =

Explanation:

Step1: Apply segment - addition postulate

Since U is between T and B, $TU + UB=TB$. Substitute the given expressions: $(4x - 1)+(2x - 1)=5x$.

Step2: Simplify the left - hand side

Combine like terms: $4x+2x-1 - 1 = 5x$, which simplifies to $6x-2 = 5x$.

Step3: Solve for x

Subtract $5x$ from both sides: $6x-5x-2=5x - 5x$, so $x - 2=0$. Then add 2 to both sides to get $x = 2$.

Step4: Find the length of TU

Substitute $x = 2$ into the expression for TU: $TU=4x - 1=4\times2-1=8 - 1=7$.

Step5: Find the length of UB

Substitute $x = 2$ into the expression for UB: $UB=2x - 1=2\times2-1=4 - 1=3$.

Step6: Find the length of TB

Substitute $x = 2$ into the expression for TB: $TB=5x=5\times2 = 10$.

Answer:

$x = 2$
$TU = 7$
$UB = 3$
$TB = 10$