Questions: Bisectors C D is the perpendicular bisector of A B. A D=6x-2 and D B=2x+18 Determine the value of x.

Transcript text: Bisectors $\overleftrightarrow{C D}$ is the perpendicular bisector of $\overline{A B}$. $A D=6 x-2$ and $D B=2 x+18$ Determine the value of $x$.

Solution

Solution Steps

Step 1: Set up the equation

Since $\overleftrightarrow{CD}$ is the perpendicular bisector of $\overline{AB}$, we know that $AD = DB$. We are given that $AD = 6x - 2$ and $DB = 2x + 18$, so we can set up the equation $6x - 2 = 2x + 18$.

Step 2: Solve for x

Subtract $2x$ from both sides: $4x - 2 = 18$. Add 2 to both sides: $4x = 20$. Divide both sides by 4: $x = 5$.