Question

points t, m, and b are collinear. point t is between m and b. mb = 4x + 20, bt = 5x - 5, and mt = 2x + 4. find the length of bt.

Explanation:

Step1: Use collinear - point property

Since $T$ is between $M$ and $B$, $MB=MT + BT$. So, $4x + 20=(2x + 4)+(5x - 5)$.

Step2: Simplify the equation

$4x + 20=2x+4 + 5x - 5$. Combine like - terms: $4x + 20=7x - 1$.

Step3: Solve for $x$

Subtract $4x$ from both sides: $20 = 3x-1$. Add 1 to both sides: $21 = 3x$. Divide both sides by 3: $x = 7$.

Step4: Find the length of $BT$

Substitute $x = 7$ into the expression for $BT$. $BT=5x - 5=5\times7 - 5=35 - 5=30$.

Answer:

30