Question

use the following information to find x. write the value of the variable.

• b is between a and c;
• ab = 3x + 6;
• bc = 15x - 2; and
• $overline{ab}congoverline{bc}$

Explanation:

Step1: Set up the equation

Since $\overline{AB}\cong\overline{BC}$, we have $3x + 6=15x - 2$.

Step2: Move like - terms together

Subtract $3x$ from both sides: $6 = 15x-3x - 2$, which simplifies to $6 = 12x - 2$.
Then add 2 to both sides: $6 + 2=12x$, so $8 = 12x$.

Step3: Solve for x

Divide both sides by 12: $x=\frac{8}{12}=\frac{2}{3}$.

Answer:

$x = \frac{2}{3}$