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CAT Properties of inequality - Practice Questions & MCQ

Edited By admin | Updated on Oct 04, 2023 04:20 PM | #CAT

Quick Facts

3 Questions around this concept.

Solve by difficulty

EASY

Solve $\frac{(x-1)(x+4)^4}{(x-3)^2}> 0$

$(1, \infty )$

$(1, \infty ) -\left \{ 3 \right \}$

$(-4,1)$

$(-4,3)$

View Solution

Concepts Covered - 1

Properties of inequality

Inequality is a mathematical statement that compares the values of two expressions using an inequality symbol such as $\mathrm{< , > , \leq or \geq . }$ The properties of inequality help us understand how to manipulate and solve inequalities.

Tips and tricks for solving inequalities:

Always remember to reverse the inequality sign when multiplying or dividing by a negative number.
If you have a compound inequality, solve each part separately and then combine the solutions using the appropriate notation (and or or).
When graphing inequalities on a number line, use an open circle for < or > and a filled circle for $\mathrm{ \leq or \geq . }$ Shade the region that includes the solutions.
When solving absolute value inequalities, consider both the positive and negative cases.
Square both sides of an inequality only if both sides are non-negative or if the inequality sign remains the same.

Examples of previous year questions:

1. Solve the inequality: $\mathrm{ 2x - 5 > 3.}$
Solution:
To solve this inequality, we isolate x by adding 5 to both sides:
$\mathrm{2x - 5 + 5 > 3 + 5}$
$\mathrm{2x > 8}$
Next, divide both sides by 2 (remembering to reverse the inequality sign because we are dividing by a negative number):
$\mathrm{x > 4}$
So, the solution to the inequality is $\mathrm{ x > 4.}$

2. Solve the compound inequality: $\mathrm{-3 \leq x < 2.}$
Solution:
This compound inequality represents values of x that are greater than or equal to -3 and less than 2. To graph this on a number line, we use a closed circle at -3 and an open circle at 2. We shade the region between these two points to represent the solutions.