Let’s take a few examples to show the steps to solve inequalities with fraction.
Question 1: - 5 x + 3 / 5 > 1 /2
Solution: -
i) (5 x * 5 + 3 * 1) / 5 > 1 / 2
(25 x + 3) / 5 > 1 / 2
2* (25 x + 3) > 1 * 5
2 * 25 x + 2 * 3 > 5
50 x + 6 > 5
50 x + 6 – 6 > 5 – 6
50 x > - 1
50 x / 50 > - 1 / 50
x > - 1 / 50
Answer: - Therefore x > - 1 / 50
Question 2: - If (3 x / 2 - 2 x / 3) < (x / 5 – 1). Find the value of x.
Solution: -
(3 x / 2 - 2 x / 3) < (x / 5 – 1)
(3x * 3 – 2 x * 2) / 6 < (x * 1 – 1 * 5) / 5
(9 x – 4 x) / 6 < (x – 5) / 5
5 x / 6 < (x – 5) / 5
5 * 5 x < 6 * (x – 5)
25 x < 6 x – 30
25 x – 6 x < 6 x – 30 – 6 x
19 x < - 30
19 x / 19 < -30 / 19
X < - 30 / 19
Answer: - Therefore x < - 30 / 19.