find and graph the solution set of (3 x - 5)/(x + 1)

We'll start by imposing contraints of existence of the
ratio. For this reason, we'll calculate the values of x for the denominator is
cancelling.

x + 1 = 0

We'll
subtract 1:

x = -1

So, for x =
-1, the ratio is indefinite.

We'll re-write the expression,
after performing the cross multiplying:

(3x - 5) <
2(x+1)

We'll remove the brackets and we'll
get:

3x - 5 < 2x +
2

We'll subtract 2x + 2 both
sides:

3x - 2x - 5 - 2 <
0

We'll combine like terms:

x
- 7 < 0

We'll add 7 both
sides:

x <
7

The ratio (3 x - 5)/(x + 1) < 2 if
and only if the values of x belong to the interval (- infinite ,
7).

Note: Since the ratio is indefinite for x
= -1, we'll reject the value -1 from the interval (- infinite ,
7).

The solution of the
inequality is the interval:

(-
infinite , 7) - {-1}.