Unlike a typical linear graph, the technique for calling out the inequality is different. The reason why linear ones are simpler (for example, 5x < 10 implies x < 2) is because the graph goes straight downwards as x decreases and never ever turns back.

For quadratic, however, the curve tends to turn as time passes. We need a different approach to solve this inequality, and this is seen by drawing a typical sketch of the quadratic function.

Nalin has shown a good attempt to this question.

An alternative way to present would be :

50x² < 72

x² < 72/50

x² < 1.44

|x|² < 1.44 since |x|² = x²

|x| < √1.44
|x| < 1.2

so -1.2 < x < 1.2

Probably almost everyone who has learnt modulus has seen the formula |x|^2 = x^2 but the vast majority would not think of it in solving such inequalities.

Exactly. That's why I show it so that the student has another technique to use in exams.

The usual would be :

x² < 1.44

x² - 1.44 < 0

x² - 1.2² < 0

(x + 1.2)(x - 1.2) < 0

Then draw the curve and shade the respective area , concluding with


-1.2 < x < 1.2

@ 'There's a Feeling' :

To answer your question, there's an inequality sign here so you cant use the usual method of :

x² = a
Then x = ± √a

Notice what happens when you do so :


if x < - 1.2 and x < 1.2 as you conclude,
then x = - 2 would be a value that satisfies it.

But this means that x² = (-2)² = 2² = 4, and 4 is bigger than 1.44.

Then x² > 1.44 since x² = 4. This contradicts the inequality that was given.


Furthermore, by saying that x < -1.2 and x < 1.2,

It just means that there's one conclusion, x < -1.2 , since x < -1.2 already implies that its smaller than 1.2

Ooo i see, thanks everyone!