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 = 2x, ub = 3x + 1, tb = 21
x =
tu =
ub =

Explanation:

Step1: Apply segment - addition postulate

Since U is between T and B, we have $TU + UB=TB$. Substituting the given expressions, we get the equation $2x+(3x + 1)=21$.

Step2: Simplify the left - hand side of the equation

Combining like terms, $2x+3x + 1=(2x+3x)+1 = 5x+1$. So the equation becomes $5x+1 = 21$.

Step3: Solve for x

Subtract 1 from both sides: $5x+1-1=21 - 1$, which gives $5x=20$. Then divide both sides by 5: $\frac{5x}{5}=\frac{20}{5}$, so $x = 4$.

Step4: Find the length of TU

Substitute $x = 4$ into the expression for TU. Since $TU = 2x$, then $TU=2\times4=8$.

Step5: Find the length of UB

Substitute $x = 4$ into the expression for UB. Since $UB=3x + 1$, then $UB=3\times4+1=12 + 1=13$.

Answer:

$x = 4$
$TU = 8$
$UB = 13$