type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar…

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. in the figure, $overline{cd}$ is the perpendicular bisector of $overline{ab}$. if the length of $overline{ac}$ is $2x$ and the length of $overline{bc}$ is $3x - 5$, the value of $x$ is

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. in the figure, $overline{cd}$ is the perpendicular bisector of $overline{ab}$. if the length of $overline{ac}$ is $2x$ and the length of $overline{bc}$ is $3x - 5$, the value of $x$ is

Answer

Answer:

5

Explanation:

Step1: Recall property of perpendicular bisector

If a line is the perpendicular bisector of a segment, any point on the perpendicular bisector is equidistant from the endpoints of the segment. So, $AC = BC$.

Step2: Set up the equation

Since $AC = 2x$ and $BC=3x - 5$, we have the equation $2x=3x - 5$.

Step3: Solve the equation

Subtract $2x$ from both sides: $0 = 3x-2x - 5$. So, $x - 5=0$. Then add 5 to both sides to get $x = 5$.