Question

f(x) = -\frac{2}{3}x + 1
g(x) = \frac{1}{3}x - 2
options:
x = -3
x = -1
x = 1
x = 3

Explanation:

Step1: Set functions equal

Set $f(x) = g(x)$:
$$-\frac{2}{3}x + 1 = \frac{1}{3}x - 2$$

Step2: Multiply by 3 to eliminate denominators

$$-2x + 3 = x - 6$$

Step3: Isolate x terms

$$-2x - x = -6 - 3$$
$$-3x = -9$$

Step4: Solve for x

$$x = \frac{-9}{-3} = 3$$

Answer:

D. $x=3$