The quetion provides two functions, that is f(x) and g(x).
For what value of x is f(x) = g(x)
We can solve this by simply equating both functions, as shown below;
[tex]\begin{gathered} f(x)=\frac{2}{3}x+5 \\ g(x)=\frac{4}{3}x+7 \\ f(x)=g(x)\text{ now becomes;} \\ \frac{2}{3}x+5=\frac{4}{3}x+7 \\ \text{Collect all like terms and we'll have} \\ \frac{2}{3}x-\frac{4}{3}x=7-5 \\ \frac{2x-4x}{3}=2 \\ -\frac{2x}{3}=2 \\ \text{Cross multiply and we'll have} \\ -x=\frac{2\times3}{2} \\ -x=3 \\ \text{Multiply both sides by -1 and we'll have} \\ -x(-1)=3(-1) \\ x=-3 \end{gathered}[/tex]The answer is, when x = 3
**Note**
Thi can also be solved graphically and at the point where the graph of both function intersect, we'll have our answer. The graphs of f(x) and g(x) is shown below;
Note that the blue line represents
[tex]f(x)=\frac{2}{3}x+5[/tex]The green line represents
[tex]g(x)=\frac{4}{3}x+7[/tex]Observe carefully that both graphs intersect at the point -3.
Therefore, the value of x that makes f(x) = g(x) is -3
