# How To Solve Inequalities

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Inequality represents two expressions including the sign >, <, ≥ and ≤.

Example of inequalities: -
·         4 x + 6 < 8
·         2 x + 4 > x
·         3 x + 9 ≤ 2 x – 1
·        X ≥ 2 x – 1

How to solve inequalities: -

Question 1: - If 4 x + 6 < 8, find the value of x.

Solution: -i)  Subtract 6 from both sides of the inequality to remove 6 from L.H.S.
(4 x + 6) – 6 < 8 -2
4 x < 6

ii)  Divide both sides by 4 to free the unknown value of x.
4 x / 4 < 6 / 4
x < 3 / 2
Therefore, x < 3 / 2.

Question 2: - If 2 x + 4 > x, find x.

Solution: -i)   Subtract x from both sides,
(2 x + 4) – x > x – x
X + 4 > 0

ii)  Subtract 4 from both sides,
(x + 4) – 4 > 0 – 4
x > - 4

Question 3: - If 3 x + 9 ≤ 2 x – 1 then find x.

Solution: -Try to keep all variable in L.H.S. and constant on R.H.S.
So we need to remove 9 from L.H.S. and 2 x from R.H.S.

i)  Subtract 9 from both sides,
(3 x + 9) – 9 ≤ (2 x – 1) – 9
3 x ≤ 2 x – 10

ii)  Subtract 2 x from sides,
3 x – 2 x ≤ (2 x – 10) – 2 x
x ≤ - 10