Question

1. 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} cong overline{bc} ).

Explanation:

Step1: Set AB equal to BC (since AB ≅ BC)

Since \( \overline{AB} \cong \overline{BC} \), their lengths are equal. So we set \( AB = BC \). Given \( AB = 3x + 6 \) and \( BC = 15x - 2 \), we have the equation:
\( 3x + 6 = 15x - 2 \)

Step2: Solve for x

Subtract \( 3x \) from both sides:
\( 6 = 12x - 2 \)

Add 2 to both sides:
\( 8 = 12x \)

Divide both sides by 12:
\( x = \frac{8}{12} = \frac{2}{3} \)

Answer:

\( x = \frac{2}{3} \)