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} \cong \overline{bc}

Explanation:

Step1: Set AB equal to BC (since they are congruent)

Since \(\overline{AB} \cong \overline{BC}\), their lengths are equal. So we set up the equation: \(4x + 7 = 20x - 5\)

Step2: Solve for x

Subtract \(4x\) from both sides: \(7 = 16x - 5\)

Add 5 to both sides: \(12 = 16x\)

Divide both sides by 16: \(x=\frac{12}{16}=\frac{3}{4}\)

Answer:

\(\frac{3}{4}\)