Question

The value of x is _____ units the lenghth of segment BC is _____ units .

Answer 1

hello

to solve this problem, we can simply write out an equation and solve for x

`\begin{gathered} AC=33 \\ AB=x+5 \\ BC=2x+10 \\ AC=AB+BC \\ 33=x+5+2x+10 \\ 33=3x+15 \\ \text{collect like terms} \\ 33-15=3x \\ 18=3x \\ \text{divide both sides by 3} \\ (3x)/(3)=(18)/(3) \\ x=6 \end{gathered}`

the value of x = 6 units

b. to solve the lenght of the segment BC.

to do this, we simply need to substitute the value of x into the equation

`\begin{gathered} BC=2x+10 \\ x=10 \\ BC=2(6)+10 \\ bc=12+10 \\ bc=22 \end{gathered}`

the value of the segment BC is equal to 22 units