To determine the value of \( x \) for which \( f(x) = g(x) \) is true, we need to set the two functions equal to each other and solve for \( x \).
The two functions are:
[tex]\[ f(x) = -3x + 4 \][/tex]
[tex]\[ g(x) = 2 \][/tex]
We want to find the value of \( x \) that makes \( f(x) \) equal to \( g(x) \). Thus, we set:
[tex]\[ -3x + 4 = 2 \][/tex]
Now, solve this equation step-by-step:
1. Start by isolating \( -3x \) on one side of the equation. To do this, subtract 4 from both sides:
[tex]\[ -3x + 4 - 4 = 2 - 4 \][/tex]
This simplifies to:
[tex]\[ -3x = -2 \][/tex]
2. Next, solve for \( x \) by dividing both sides of the equation by \(-3\):
[tex]\[ x = \frac{-2}{-3} \][/tex]
3. Simplify the right-hand side:
[tex]\[ x = \frac{2}{3} \][/tex]
Therefore, the value of \( x \) that makes \( f(x) \) equal to \( g(x) \) is:
[tex]\[ x = \frac{2}{3} \][/tex]
So, the solution is:
[tex]\[ x = 0.6666666666666666 \][/tex]
