Question

1. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value.

x =
bc =
cd =
bd =

Explanation:

Step1: Use segment - addition postulate

Since $BD = BC + CD$, we have the equation $(7x - 10)=(4x - 29)+(5x - 9)$.

Step2: Simplify the right - hand side

$(4x - 29)+(5x - 9)=4x+5x-29 - 9=9x-38$. So the equation becomes $7x - 10=9x - 38$.

Step3: Solve for x

Subtract $7x$ from both sides: $-10 = 9x-7x - 38$, which simplifies to $-10 = 2x - 38$. Then add 38 to both sides: $-10 + 38=2x$, so $28 = 2x$. Divide both sides by 2, we get $x = 14$.

Step4: Find BC

Substitute $x = 14$ into the expression for $BC$: $BC=4x - 29=4\times14 - 29=56 - 29 = 27$.

Step5: Find CD

Substitute $x = 14$ into the expression for $CD$: $CD=5x - 9=5\times14 - 9=70 - 9 = 61$.

Step6: Find BD

Substitute $x = 14$ into the expression for $BD$: $BD=7x - 10=7\times14 - 10=98 - 10 = 88$.

Answer:

$x = 14$
$BC = 27$
$CD = 61$
$BD = 88$