# Rules of Inequalities

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Inequality is the equation which has less than or greater than symbols in it i.e. '<' and '>' respectively. Equality is when we can equate both sides of the equation and is represented by ‘=’. The greater that sign in an inequality ‘>’ signifies that the left hand side of the equation is greater that the right hand side. The lesser that sign in an inequality ‘<’ signifies that the left hand side of the equation is lesser that the right hand side. Linear inequalities is the inequalities where the degree of the variables is one.

Example 1: Find the solution of the linear inequality 4 x + 2 > 14?

Solution: Given is the equation with one unknown variables x.
Here, 4 x + 2 > 14 is a linear inequality with greater than sign.
Subtract 2 on both sided of the equation.
4 x +2 -2 > 14 - 2; 4 x > 12;
Now divide by 4 on both sides of the equation.
4 x/4 > 12 / 4; x > 3.
Hence the solution to the linear inequality is x > 3.

Example 2: Find the solution of the linear inequality 8 z - 6 < 34?

Solution: Here 8 z - 6 < 34 is a linear inequality with less than sign.
Add 6 on both sided of the equation.
8 z - 6 + 6 < 34 + 6; 8 z < 40;
Now divide by 8 on both sides of the equation.
8 z/8 < 40/8; z < 5.

Hence the solution to the linear inequality is z < 5.