Question

Line AB is a perpendicular bisector of CD find the value of x

Answer 1

x = 5

Step-by-step explanation

As shown in the figure, the two segments from C to the intersection with AB and from the intersection to D are congruent. This means that they have the same length:

`2x+3=5x-12`

We have this equation that we can solve for x.

First we need that all the terms that contain x are on the same side of the equation. Subtract 2x from both sides:

`\begin{gathered} 2x-2x+3=5x-2x-12 \\ 3=3x-12 \end{gathered}`

Now we need that all the terms that don't contain x on the same side as well. Add 12 on both sides of the equation:

`\begin{gathered} 3+12=3x-12+12 \\ 15=3x \end{gathered}`

Finally, to find x, divide both sides by 3:

`\begin{gathered} (15)/(3)=(3x)/(3) \\ 5=x \end{gathered}`

The value of x is 5.