The term inequality applies to any statement involving one of the symbols<,>,≤,≥. Similar to ordinary equations, inequality equations too have solutions

## Rules for finding the solutions to inequality equations

- Add or subtract at the same expression or number to both sides of the inequality and preserve the inequality sign.
- Multiply or divide both sides of the inequality by the same positive number and preserve the inequality sign.
- Multiply or divide both sides of the inequality by the same negative number and reverse the inequality sign.

The expression 3x – 1 > x + 1 is a linear inequality in one variable x. Thus, a linear inequality in x is an inequality in which the highest power of x is one (unity).

Solve the following linear inequality and represent them on a number line.

A number line is used to illustrate linear inequalities in one variable. A point x = a divides the number line into 2 parts, x < a and x > a

1. 4x + 8 < 3x + 16

Subtract 8 from both sides

4x + 8 – 8 < 3x – 8 + 16

4x < 3x + 8

Subtract 3x from both sides

4x – 3x < 3x + 8 – 3x

X < + 8

ii. 3 (x – 6) ≤ 9 (x – 1)

open the brackets

3x – 18 ≤ 9x – 9

Collect like terms

3x – 9x ≤ -9 + 18

-6x ≤ + 9

Divide through by -6 and change the sign.

(-6x)/(-6 ) ≥ (-9)/6

X ≥ (-3)/2

(x ≥ 23/7)

iii. 5 (x + 2) – 2(4x -1) > 6(2x -3)

iv. (5x-1)/3- (1-2x)/5 ≤8+x

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