Verified answer

We cannot just multiply both sides by x + 1 like that without considering the sign of x + 1, like the first answerer did. The fact that the denominator is undefined at x = -1 does not make any number less than -1 not a solution.

Recall that if we multiply both sides by a positive number, we can do so without switching the direction of the inequality. However, if we multiply both sides by a negative number, we must switch the sign.

If we assume that x + 1 > 0 <==> x > -1, we can multiply across to get:

(2x - 3)/(x + 1) ≤ 1

==> 2x - 3 ≤ x + 1

==> x ≤ 4.

Combining this with the fact that x > -1 gives -1 < x ≤ 4.

If we assume that x + 1 < 0 <==> x < -1, we have:

(2x - 3)/(x + 1) ≤ 1

==> 2x - 3 ≥ x + 1

==> x ≥ 4.

However, we assumed that x < -1 here and thus all solutions produced by this case are discarded.

Therefore, the solution is -1 < x ≤ 4.

I hope this helps!

you first could desire to get X via itself. to try this subtract the three away. So now you have 2X=-2 The to get the X thoroughly via itself you divide the two away (on the grounds this is the guideline, to divide). So X =-a million (and that's in view which you divided the two remote from the X and on the different facet it grew to become into divided via the -2. wish that helps.

(2*x - 3)

------------ ≤ 1

(x + 1)

2*x - 3 ≤ x + 1

2*x - x ≤ 1 + 3

x ≤ 4

As x can't be = - 1 (because the indetermination), the solution is - 1 < x ≤ 4