# Solve Inequalities

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Inequality is the equation which has less than or greater than symbols in it i.e. '<' and '>' respectively. Linear inequalities is the inequalities where the degree of the variables is one. An inequality equation can contain variables, constants and exponents for the variables. There are different mathematical operations that can be used in an inequality like addition, subtraction, multiplication and division.

Example 1: Find the solution of the inequality equation 4 x - 5 > 15?

Solution: Given is the inequality equation with one unknown variables x.
4 x - 5 > 15 is a linear inequality with greater than sign.
Add 5 on both sided of the equation.
This gives, 4 x - 5 + 5 > 15 + 5; 4 x > 20;
Now divide the inequality by 4 on both sides of the equation.
4 x/ 4 > 20 /4; x > 5.

Hence the solution to the linear inequality is x > 5.

Example 2: Find the solution of the inequality equation 6 x - 8 < 10?

Solution: Given is the inequality equation with one unknown variables x.
6 x - 8 < 10 is a linear inequality with lesser than sign.
Add 8 on both sided of the equation.
This gives, 6 x - 8 + 8 < 10 + 8; 6 x < 18;
Now divide the inequality by 4 on both sides of the equation.
6 x/ 6 < 16 /8; x < 3.

Hence the solution to the linear inequality is x < 3.