Solve the following linear inequations in R(5-2x)/3 < x/6 - 5\(\frac{5

1.	Solve the following linear inequations in R(5-2x)/3 < x/6 - 5\(\frac{5-2x}{3}\) < \(\frac{x}{6}\) - 5
Answer» Given, (5-2x)/3 < x/6 - 5 ⇒ \(\frac{5-2x}{3}\) < \(\frac{x-30}{6}\) ⇒ 2(5 – 2x) < x – 30 ⇒ 10 – 4x < x – 30 ⇒ 10 – 4x – 10 < x – 30 – 10 ⇒ –4x < x – 40 ⇒ x – 40 > –4x ⇒ x – 40 + 40 > –4x + 40 ⇒ x > –4x + 40 ⇒ x + 4x > –4x + 40 + 4x ⇒ 5x > 40 ⇒ \(\frac{5x}{5}\) > \(\frac{40}{5}\) ∴ x > 8 Thus, The solution of the given inequation is (8, ∞).

Solve the following linear inequations in R(5-2x)/3 < x/6 - 5\(\frac{5-2x}{3}\) < \(\frac{x}{6}\) - 5

Answer»

Given,

(5-2x)/3 < x/6 - 5

⇒ \(\frac{5-2x}{3}\) < \(\frac{x-30}{6}\)

⇒ 2(5 – 2x) < x – 30

⇒ 10 – 4x < x – 30

⇒ 10 – 4x – 10 < x – 30 – 10

⇒ –4x < x – 40

⇒ x – 40 > –4x

⇒ x – 40 + 40 > –4x + 40

⇒ x > –4x + 40

⇒ x + 4x > –4x + 40 + 4x

⇒ 5x > 40

⇒ \(\frac{5x}{5}\) > \(\frac{40}{5}\)

∴ x > 8

Thus,

The solution of the given inequation is (8, ∞).