F(x)=3/2x-3 g(x)=5x+4 determine where f(x)=g(x)

x = -2

Step-by-step 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.

the answer is simply just 6n add the two together as they have an n