# Linear Inequalities Class 11

Linear Inequalities class 11 – Two algebraic expressions or real numbers related by the symbol $\leq, \;\geq , \;< , \;and\;>$ 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, ∞).

1. 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

#### Practise This Question

The number of observations in a group is 40.  If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is