Two algebraic expressions joined using any of these inequality symbols <, >,  ≤, and ≥ are called algebraic inequalities or algebraic inequations. If the degree of the inequation is 1 then it is called linear inequality.

Inequality symbolMeaning
<Less than
>Greater than
≤ Less than or equal to
≥greater than or equal to

x = 3 means value of x is equal to 3.

x ≥ 3 means x is equal to three or more

value a number x at most 3 means x ≤ 3

Value of a number x at least 3 means x ≥ 3

How to solve Linear Inequalities (Inequations)

Addition and subtraction rule for algebraic equations are same for inequalities.

If you Multiply or divide by negative number, reverse the inequality symbol

Solve the following inequalities

  1. 3 (x – 1)< 6 
     3x - 3 <  6
         +3   +3
___________________
     3x     <  9
          
\frac{3x}3 <  \frac {9}3

x < 3

x<3 on number line

2. Solve the following inequality

4+2\frac{5}{6}x\le 5+3x
4+\frac{17}{6}x\le \:5+3x
\frac{17}{6}x\le \:3x+1
6 (\frac{17}{6}x)\le \:6(3x+1)
17x \le 18x+6
-x\le 6

x\ge-6
\begin{bmatrix}\mathrm{Solution:}\:&\:x\ge \:-6\:\\ \:\mathrm{Interval\:Notation:}&\:[-6,\:\infty \:)\end{bmatrix}