To find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is true, let's follow these steps in detail:
1. Define the Functions:
- We are given [tex]\( f(x) = -3x + 4 \)[/tex]
- And [tex]\( g(x) = 2 \)[/tex]
2. Set the Functions Equal:
- Since we want to find the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex], we set the two expressions equal to each other:
[tex]\[ -3x + 4 = 2 \][/tex]
3. Isolate the Variable [tex]\( x \)[/tex]:
- To solve for [tex]\( x \)[/tex], we first need to isolate [tex]\( x \)[/tex] on one side of the equation. Start by getting all constants on one side:
[tex]\[ -3x + 4 - 4 = 2 - 4 \][/tex]
- Simplify both sides:
[tex]\[ -3x = -2 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Now, divide both sides by -3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-2}{-3} \][/tex]
5. Simplify the Expression:
- Simplifying the fraction, we get:
[tex]\[ x = \frac{2}{3} \][/tex]
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[ x = 0.6666666666666666 \approx \frac{2}{3} \][/tex]
