Question

Which of the following values are solutions to the inequality minus, 1, is less than or equal to, 1, minus, 2, x, question mark−1≤1−2x? I., 2, II., minus, 6, III., 1 I.2II.−6III.1

Answer 1

To find the solutions to the inequality -1 ≤ 1 - 2x, we can solve it step by step:

-1 ≤ 1 - 2x

First, let's isolate the variable by subtracting 1 from both sides:

-1 - 1 ≤ 1 - 1 - 2x

-2 ≤ -2x

Next, divide both sides by -2. Remember that when dividing by a negative number, the inequality sign flips:

-2/(-2) ≥ -2x/(-2)

1 ≥ x

So, the inequality is satisfied when x is less than or equal to 1.

Now let's check the given options:

I. 2: Since 2 is greater than 1, it does not satisfy the inequality.

II. -6: Since -6 is less than 1, it satisfies the inequality.

III. 1: Since 1 is equal to 1, it satisfies the inequality.

Therefore, the correct solutions to the inequality are II. -6 and III. 1.