Question

segments practice - equations
a---b---c (with ab labeled (7x - 6), bc labeled (12 - 2x))
b is the midpoint of ac.
(x = square)
(ab = square)
(bc = square)
(ac = square)

Explanation:

Step1: Use midpoint property (AB = BC)

Since B is the midpoint of AC, \( AB = BC \). So, \( 7x - 6 = 12 - 2x \).

Step2: Solve for x

Add \( 2x \) to both sides: \( 7x + 2x - 6 = 12 \), which simplifies to \( 9x - 6 = 12 \). Then add 6 to both sides: \( 9x = 12 + 6 = 18 \). Divide both sides by 9: \( x = \frac{18}{9} = 2 \).

Step3: Calculate AB

Substitute \( x = 2 \) into \( AB = 7x - 6 \): \( AB = 7(2) - 6 = 14 - 6 = 8 \).

Step4: Calculate BC

Since \( AB = BC \), \( BC = 8 \) (or substitute \( x = 2 \) into \( 12 - 2x \): \( 12 - 2(2) = 12 - 4 = 8 \)).

Step5: Calculate AC

\( AC = AB + BC = 8 + 8 = 16 \) (or use \( AC = 2 \times AB = 2 \times 8 = 16 \)).

Answer:

\( x = 2 \)
\( AB = 8 \)
\( BC = 8 \)
\( AC = 16 \)