Question

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

• b is between a and c;
• ab = 4x + 7
• bc = 20x - 5 and
• $overline{ab}congoverline{bc}$

Explanation:

Step1: Set up the equation

Since $\overline{AB}\cong\overline{BC}$, we have $4x + 7=20x - 5$.

Step2: Move x - terms to one side

Subtract $4x$ from both sides: $7 = 20x-4x - 5$.
Simplify to get $7 = 16x - 5$.

Step3: Isolate the x - term

Add 5 to both sides: $7 + 5=16x$, so $12 = 16x$.

Step4: Solve for x

Divide both sides by 16: $x=\frac{12}{16}=\frac{3}{4}$.

Answer:

$x = \frac{3}{4}$