Solve the following linear inequations in R(4+2x)/3 ≥ x/2 - 3\(\frac

1.	Solve the following linear inequations in R(4+2x)/3 ≥ x/2 - 3\(\frac{4+2x}{3}\) ≥ \(\frac{x}{2}\) - 3
Answer» Given, (4+2x)/3 ≥ x/2 - 3 ⇒ \(\frac{4+2x}{3}\) ≥ \(\frac{x-6}{2}\) ⇒ \((\frac{4+2x}{3})\) \(\times\) 3 \(\times\) 2 ≥ \((\frac{x-6}{2})\) \(\times\) 3 \(\times\) 2 ⇒ 2(4 + 2x) ≥ 3(x – 6) ⇒ 8 + 4x ≥ 3x – 18 ⇒ 8 + 4x – 8 ≥ 3x – 18 – 8 ⇒ 4x ≥ 3x – 26 ⇒ 4x – 3x ≥ 3x – 26 – 3x ∴ x ≥ –26 Thus, The solution of the given inequation is [–26, ∞).

Solve the following linear inequations in R(4+2x)/3 ≥ x/2 - 3\(\frac{4+2x}{3}\) ≥ \(\frac{x}{2}\) - 3

Answer»

Given,

(4+2x)/3 ≥ x/2 - 3

⇒ \(\frac{4+2x}{3}\) ≥ \(\frac{x-6}{2}\)

⇒ \((\frac{4+2x}{3})\) \(\times\) 3 \(\times\) 2 ≥ \((\frac{x-6}{2})\) \(\times\) 3 \(\times\) 2

⇒ 2(4 + 2x) ≥ 3(x – 6)

⇒ 8 + 4x ≥ 3x – 18

⇒ 8 + 4x – 8 ≥ 3x – 18 – 8

⇒ 4x ≥ 3x – 26

⇒ 4x – 3x ≥ 3x – 26 – 3x

∴ x ≥ –26

Thus,

The solution of the given inequation is [–26, ∞).