Question

Question 1

1 pts
Which can you use to find the solution.
set for 2|1x|+ 1 ≥ 3?
01-x≤-1 OR 1 − x ≥ 1
01-x-1 AND 1 - x ≤ 1
01-x-1 OR 1 - x ≤ 1
01-x≤-1 AND 1 - x ≥1

Answer 1

The solution to the inequality 2|1x| + 1 ≥ 3 involves isolating the absolute value on one side and considering two cases based on the absolute value definition. These cases lead to the solution set: 1-x ≤ -1 OR 1 - x ≥ 1.

Step-by-step explanation:

To solve the inequality 2|1x| + 1 ≥ 3, first isolate the absolute value expression on one side:

1. Subtract 1 from both sides: 2|1x| ≥ 2.
2. Divide by 2: |1x| ≥ 1.
3. Next, consider the definition of the absolute value, which states that |x| = x if x ≥ 0, and |x| = -x if x < 0. This gives us two cases:
4. Case 1: 1x ≥ 1, which simplifies to x ≥ 1.
5. Case 2: 1x ≤ -1, which simplifies to x ≤ -1.

The solution to the inequality is the set where either case is true hence, the correct answer is:

1-x ≤ -1

OR

1 - x ≥ 1