Question

bd = 67, bc = 3x + 5, and cd = 4x + 6. find x, bc, and cd.

Explanation:

Step1: Set up equation

Since $BD = BC+CD$, we have $67=(3x + 5)+(4x + 6)$.

Step2: Simplify the right - hand side

Combine like terms: $67 = 3x+4x + 5+6$, so $67=7x + 11$.

Step3: Solve for x

Subtract 11 from both sides: $67−11=7x$, which gives $56 = 7x$. Then divide both sides by 7: $x=\frac{56}{7}=8$.

Step4: Find BC

Substitute $x = 8$ into the expression for $BC$: $BC=3x + 5=3\times8+5=24 + 5=29$.

Step5: Find CD

Substitute $x = 8$ into the expression for $CD$: $CD=4x + 6=4\times8+6=32+6=38$.

Answer:

$x = 8$, $BC = 29$, $CD = 38$