ANSWER
x = 5
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:
[tex]2x+3=5x-12[/tex]
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:
[tex]\begin{gathered} 2x-2x+3=5x-2x-12 \\ 3=3x-12 \end{gathered}[/tex]
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:
[tex]\begin{gathered} 3+12=3x-12+12 \\ 15=3x \end{gathered}[/tex]
Finally, to find x, divide both sides by 3:
[tex]\begin{gathered} \frac{15}{3}=\frac{3x}{3} \\ 5=x \end{gathered}[/tex]
The value of x is 5.
