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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

Solve \frac{(x-1)(x+4)^4}{(x-3)^2}>0

Concepts Covered - 1

Properties of inequality

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.

 

 

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