Question

1. if ab = 18 and ac = 3x + 6, then x =?

Explanation:

Step1: Identify equal - length segments

Since B is the mid - point of AC, we know that AB = BC and AC=2AB.

Step2: Set up the equation

Given AB = 18 and AC = 3x + 6, and AC = 2AB. Substitute AB = 18 into the equation for AC: 3x+6=2×18.

Step3: Simplify the right - hand side

2×18 = 36, so the equation becomes 3x+6 = 36.

Step4: Isolate the variable term

Subtract 6 from both sides of the equation: 3x+6 - 6=36 - 6, which simplifies to 3x = 30.

Step5: Solve for x

Divide both sides of the equation 3x = 30 by 3: $\frac{3x}{3}=\frac{30}{3}$, so x = 10.

Answer:

10