Question

1. solve for (x) if (\triangle abc) is isosceles.

Explanation:

Identify equal sides

The tick marks on sides \(AC\) and \(BC\) indicate they are equal.

$$AC = BC$$

Set up the equation

Substitute the given algebraic expressions for the side lengths.

$$x + \frac{1}{3} = 2x - \frac{1}{3}$$

Solve for x

Subtract \(x\) from both sides of the equation.

$$\frac{1}{3} = x - \frac{1}{3}$$

Isolate the variable

Add \(\frac{1}{3}\) to both sides to find \(x\).

$$x = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$$

Answer:

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