Solve the inequalities in Exercises 5 to 16 for real x:
3 (2 – x) ≥ 2 (1 – x)

Question

Solve the inequalities in Exercises 5 to 16 for real x: 3 (2 – x) ≥ 2 (1 – x)

Philoid · Accepted Answer

It is given in the question that,

3 (2 – x) ≥ 2 (1 – x)

6 – 3x ≥ 2 – 2x

Adding 2x to both the sides,

6 – 3x+ 2x ≥ 2 – 2x+ 2x

6 – x≥ 2

Subtracting 6 from both the sides,

6 – x – 6 ≥2 – 6

- x ≥-4

x ≥ 4

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

Thus, [4, ∞) is the required solution set.

Solve the inequalities in Exercises 5 to 16 for real x:3 (2 – x) ≥ 2 (1 – x)