# Solving compound 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 than 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 6 x - 3 > 15?
Solution: Given is the equation with one unknown variables x.
Here, 6 x - 3 > 15 is a linear inequality with greater than sign.
Adding 3 on both sided of the equation.
6x +3 -3 > 15 + 3; 6 x > 18;
Now divide by 6 on both sides of the equation.
6 x/6 > 18 / 6; x > 3.
Hence the solution to the linear inequality is x > 3.

Example 2: Find the solution of the linear inequality 18 z - 6 < 30?
Solution: Here 18 z - 6 < 30 is a linear inequality with less than sign.
Add 6 on both sided of the equation.
18 z - 6 + 6 < 30 + 6; 18 z < 36;
Now divide by 8 on both sides of the equation.
8 z/8 < 36/18; z < 2.
Hence the solution to the linear inequality is z < 2.