Answer:
x = -2
Explanation:
I am not sure you typed this correctly.
the way you wrote this, it says
f(x) = (3/2)x - 3
but I suspect you mean
f(x) = 3/(2x) - 3
our even
f(x) = 3/(2x - 3)
I assume the last one.
3/(2x - 3) = 5x + 4
that is what is meant by f(x)=g(x) : find out the value(s) of x for which the y/result values of both functions are the same.
so, then we can transform
3 = (5x + 4)×(2x - 3)
3 = 10x² -15x + 8x - 12
10x² - 7x - 15 = 0
and this can be solved by the solution squared equations :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here
a = 10
b = -7
c = -15
so,
x = (7 ± sqrt(49 - 4×10×-15))/20 = (7 ± sqrt(49+600))/20 =
≈ (7 ± 25.48)/20
x1 = -18.48/20
x2 = 32.48/20
these are really not nice numbers for a homework or such.
so, let's try the next interpretation of what you wrote.
f(x) = 3/(2x) - 3
3/(2x) - 3 = 5x + 4
3/(2x) = 5x + 7
3 = 10x² + 14x
10x² + 14x - 3 = 0
a = 10
b = 14
c = -3
x = (-14 ± sqrt(196 - 4×10×-3))/20 =
= (-14 ± sqrt(196 + 120))/20 = (-14 ± 17.78)/20
that did not give any good numbers either.
so, next attempt :
f(x) = (3/2)x - 3 = 3x/2 - 3
3x/2 - 3 = 5x + 4
3x/2 = 5x + 7
3x = 10x + 14
7x = -14
x = -2
ok, so it seems the first, original interpretation was correct. sorry.
but just in case, please use the other 2 approaches if and as needed.