Linear Inequalities Class 11

Linear Inequalities Class 11 Concept

Two algebraic expressions or real numbers related by the symbol \(\leq, \;\geq , \;< , \;and\;>\) i.e., greater than, less than, or greater than and less than symbols forms an inequality. For example: px + qy > 0, 9a – 21b < 0, etc. From an equality Equal numbers can be subtracted or added from both the sides of an equation. Also, both sides of an inequality can be divided or multiplied by the same number (non-zero).

1. Solve \(4x + 3 < 6x +7\)

Solution: Given \(4x + 3 < 6x +7\)

Therefore, 3 – 7 < 6x – 4x or, 2x > – 4, i.e. x > -2

Hence, the solution of given inequality is (–2, ∞).

2. Solve \(\frac{5-2x}{3}\leq \frac{x}{6}-5\)

Solution: Given \(\frac{5-2x}{3}\leq \frac{x}{6}-5\)

Therefore, \(10-4x\leq x-30\)

Or, \(-5x\leq -40\;\;or\;\;x\geq 8\)

Therefore, all real numbers equal to or greater than 8 are the solutions of the

given inequality i.e.\(x \in [8, \infty )\)

Linear Inequalities class 11 Examples

Linear Inequalities Class 11
Linear Inequalities Class 11
Linear Inequalities Class 11
Linear Inequalities Class 11
Linear Inequalities Class 11
Linear Inequalities Class 11

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Practise This Question

A die is rolled and the outcomes are observed. Event A is an even number turns up and event B is a prime number turns up. Match the events on left with the outcomes on right.

1.Event A or BP.14, 6}2.Event A and BQ.12}3.Event A but not BR.12,3,4,5,6,}4.Complementary event of BS.11,4,6}

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