Question

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

bd =
cd =
bc =
x =

Explanation:

Step1: Set up the equation

Since $BD = BC + CD$, we substitute the given expressions: $7x - 10=(4x - 29)+(5x - 9)$.

Step2: Simplify the right - hand side

Combine like terms on 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: $7x - 10-7x=9x - 38-7x$, which simplifies to $- 10 = 2x-38$. Then add 38 to both sides: $-10 + 38=2x-38 + 38$, giving $28 = 2x$. Divide both sides by 2: $\frac{28}{2}=\frac{2x}{2}$, so $x = 14$.

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:

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