Question

Help would be appreciated :)

Consider the equality x - 1/ x + 1 < 3. When solving this inequality, should the inequality sign change direction? Why or why not?

Thanks c:

Answer 1

it will change direction because to solve it you need to multiply by the square of the denominator

Answer 2

The inequality sign should change direction when

i). Multiplying or dividing both sides of an inequality by a negative,
ii). reading an inequality backwards, or
iii). when taking the reciprocal of both sides iff both sides are of the same sign (positive or negative).

Answer 3

Sorry, my internet is having issues.

Answer 4

this is how I would solve this inequality.

start with x cannot equal - 1

mulltiply both sides by the square of the denominator

\[\frac{x -1}{x + 1} \times (x + 1)^2 < 3\times (x + 1)^2\]

which becomes

\[x^2 - 1 < 3x^2 + 6x + 3\]

or

\[-2x^2 - 6x - 4 < 0\]

multiply by -1/2 will reverse the inequality

\[x^2 + 3x + 2 > 0\]

\[(x + 2)(x + 1) > 0\]

so the possible solutions are x = -2 and x = -1

now test the solution



hope it helps