Question

State whether the following statement is true or false: The inequality x≥−2x≥−2 has the set of real numbers as its solution set.

a) True
b) False

Answer 1

The statement 'x ≥ -2x' is false; when solved, the inequality x ≥ 0 shows the solution is not the set of all real numbers, but only those greater than or equal to zero.

Step-by-step explanation:

The statement 'x ≥ -2x' is false. To assess whether the set of real numbers is the solution set for this inequality, we need to solve it.

Let's solve the inequality step by step:

1. Add 2x to both sides of the inequality to get 3x ≥ 0.
2. Divide both sides by 3 to get x ≥ 0.

This means that the solution set for the inequality is not all real numbers, but rather all real numbers that are greater than or equal to zero.