Inequality

-5/4>= x >= 5/2

-5/2>= x >= 5/2

x-3|x| > +5 (Removing Mod, you get +/_5)

x + 3x > +5

So,

x + 3x > +5 (or) x-3x > +5

4x> +5 (or) 2x< +5

From here you could draw a number line and find the intersecting section of both is -5/4> x > 5/2

shankar.ashwin wrote:x-3|x| > +5 (Removing Mod, you get +/_5)

x + 3x > +5

So,

x + 3x > +5 (or) x-3x > +5

4x> +5 (or) 2x< +5

From here you could draw a number line and find the intersecting section of both is -5/4> x > 5/2

This inequality suggests that x is greater than or equal to 2.5 but less than or equal to -1.25. Shouldn't it be x>=5/2 or x<=-5/4 in one case and x<=-5/2 or x >= 5/4 ?

seema19 wrote:How to identify the limits of this inequality?

|x - 3|x|| >= 5

[Mod x minus 3 mod x greater than or equal to 5.]

Basic learning is that if |n| ≥ 5, then there are only two possibilities viz. either n ≥ 5 or n ≤ -5. Therefore in the present case,

EITHER

x - 3|x| ≥ 5 → 3|x| ≤ x – 5

→ either 3 x ≤ x – 5 → x ≤ -5/2 or 3 x ≥ -x + 5 → x ≥ 5/4.

OR

x - 3|x| ≤ -5 → 3|x| ≥ x + 5

→ either 3 x ≥ x + 5 → x ≥ 5/2 or 3 x ≤ -x – 5 → x ≤ -5/4.

We may now safely pick x ≥ 5/2 and x ≤ -5/4 as the intervals that best explain the Absolute Value Inequality |x - 3|x|| ≥ 5.

Note: Please read → as "implies that". Formatting problem!