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    CAT Solving inequalities using number line - Practice Questions & MCQ

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

    Quick Facts

    • 6 Questions around this concept.

    Solve by difficulty

    QuestionEASY

    The solution of the inequality  2(x-1)>x+4 is:

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    Solution of the inequation -2(x+4)\leq x+5 is:

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    Which values of $x$ satisfy the inequality $(x + 1)(x - 3) < 0$?

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    The solution of the inequality $\:\left(x\:+\:1\right)\left(x\:-\:2\right)\left(x+7\right)\:<\:0$ is:

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    Solution of $(x+1)(x-2)\geq 0$ is:

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    Concepts Covered - 1

    Solving inequalities using number line

    1. Introduction

    • Definition of Inequalities
    • Key elements of inequalities
    • Representation of inequalities using number line

     

    2. Solving Inequalities using Number Line

    • Step by step method for solving inequalities using number line
    • Example using previous year questions:
    • Question: Solve the inequality \mathrm{3x + 4 > 10}
    • Solution:
      • Step 1: Subtract 4 from both sides of the inequality. \mathrm{3x > 6}
      • Step 2: Divide both sides by \mathrm{3. x > 2}
      • Step 3: Represent the solution on the number line.

    3. Tips and Tricks

    • Tip 1: Be careful while performing operations on both sides of the inequality. The direction of the inequality may change.
    • Tip 2: Remember to flip the inequality sign when multiplying or dividing by a negative number.
    • Tip 3: Use the number line to visualise the solution and identify the valid range.

    4. Common Mistakes to Avoid

    • Mistake 1: Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
    • Mistake 2: Confusing the direction of the inequality while performing operations on both sides.
    • Mistake 3: Misinterpreting the solution on the number line.

    5. Practice Questions

    • Question 1: Solve the inequality \mathrm{2x - 5 \leq 9}
    • Question 2: Solve the inequality \mathrm{3(2 - x) > 8 - 2x}

    6. Key Takeaways

    • Understanding and solving inequalities using the number line
    • Applying the steps to solve inequalities in management entrance exam questions

    Study other Related Concepts

    CAT Solving inequalities using number line Current Topic

    CAT Solving linear Equations in two variables (equations of the form of ax + by +c = 0)
    CAT Area between the lines
    CAT Equations of the form of ax2 + by +c = 0
    CAT Concept of roots, sum of roots and product of roots
    CAT Nature of roots
    CAT Quadratic formula
    CAT Solving inequalities using number line
    CAT Properties of inequality
    CAT Concept of finding maximum and minimum values
    CAT Concept of range

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