To solve for the value of [tex]\( x \)[/tex] where [tex]\( f(x) = g(x) \)[/tex], we need to set the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] equal to each other and solve for [tex]\( x \)[/tex].
Given:
[tex]\[ f(x) = -3x + 4 \][/tex]
[tex]\[ g(x) = 2 \][/tex]
We set [tex]\( f(x) = g(x) \)[/tex]:
[tex]\[ -3x + 4 = 2 \][/tex]
Now, solve for [tex]\( x \)[/tex]:
1. Subtract 4 from both sides of the equation:
[tex]\[ -3x + 4 - 4 = 2 - 4 \][/tex]
[tex]\[ -3x = -2 \][/tex]
2. Divide both sides by -3 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-2}{-3} \][/tex]
[tex]\[ x = \frac{2}{3} \][/tex]
Thus, the value of [tex]\( x \)[/tex] for which [tex]\( f(x) = g(x) \)[/tex] is:
[tex]\[ x = \frac{2}{3} \][/tex]
