Question

Solve the given inequality for real x: 3(2 – x) ≥ 2(1 – x)

Answer 1

3(2 – x) ≥ 2(1 – x) ⇒ 6 – 3x ≥ 2 – 2x ⇒ 6 – 3x + 2x ≥ 2 – 2x + 2x ⇒ 6 – x ≥ 2 ⇒ 6 – x – 6 ≥ 2 – 6 ⇒ –x ≥ –4 ⇒ x ≤ 4 Thus, all real numbers x, which are less than or equal to 4, are the solutions of the given inequality. Hence, the solution set of the given inequality is (–∞, 4].

mrk as brainlist plzzz.....

Answer 2

Solution :-

Given that, 3 (2 – x) ≥ 2 (1 – x)

By multiplying we get

6 – 3x ≥ 2 – 2x

Now by adding 2x to both the sides,

6 – 3x + 2x ≥ 2 – 2x + 2x

6 – x ≥ 2

Again by subtracting 6 from both the sides, we get

6 – x – 6 ≥ 2 – 6

– x ≥ – 4

Multiplying throughout inequality by negative sign we get

x ≤ 4

∴ The solutions of the given inequality are defined by all the real numbers greater than or equal to 4.

Hence the required solution set is (- ∞, 4]