# How To Solve Linear Inequalities

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Inequality symbol means > (greater than), < (less than), ≥ (greater than equal to) and ≤ (less than equal to).

Hence linear inequalities are the expression included with these symbols.

How to solve linear inequalities: -

Let us consider a few mathematical problems to show the steps to solve linear inequalities.

Question 1: - Solve 5 x – 8 < 9.

Solution: -
5 x – 8 < 9
Or, 5 x – 8 + 8 < 9 + 8
Or, 5 x < 17
Or, 5 x / 5 < 17 / 5
Or, x < 17 / 5
Therefore, x < 17 / 5.

Question 2: - Solve (3 x + 5 ) / (2 x + 1) > 1

Solution: -
(3 x + 5) / (2 x + 1) > 1
Or,       (3 x + 5) > (2 x + 1)
Or,       (3 x + 5)- 5 > (2 x + 1) – 5
Or,       3 x > 2 x – 4
Or,       3 x – 2 x > (2 x – 4) – 2 x
Or,       x > - 4
Therefore x > - 4

Question 3: - Solve 3 (x – 1) < 2 x

Solution: -
3 (x – 1) < 2 x
Or,       3 * x – 3 * 1 < 2 x
Or,       3 x – 3 < 2 x
Or,       (3 x – 3) + 3 < 2 x + 3
Or,       3 x < 2 x + 3
Or,       3 x – 2 x < (2 x + 3) – 2 x
Therefore x < 3