Systems of Absolute Inequalities | 3 &#x2212;<!-- − --> 2 x | &#x2265;<!-- ≥

Callum Dudley

Callum Dudley

Answered question

2022-06-30

Systems of Absolute Inequalities
| 3 2 x | 1
x 2 / ( x + 2 ) 0
Please advise on this with the answer to this.

Answer & Explanation

jugf5

jugf5

Beginner2022-07-01Added 18 answers

x = 0 is also a possible solution, the solution set is therefore x < 2  or  x = 0 or x < 2  or  x = 0
Here's the proof:
We first focus on the second inequality: x 2 x + 2 0 implies that either the nominator or the denominator are negative (not both). Or that the nominator is equal to 0. The denominator is never negative. Hence we are left with x = 0 (nominator is zero). Or x < 2 (denominator negative). We can plug in all these into the first inequality and see that they all hold.

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