Question

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.

1 ≥ 2x
6x ≥ 3 + 8x – 4

Answer 1

1 ≥ 2x

6x ≥ 3 + 8x - 4

and the first line graph.

Explanation:

6x ≥ 3 + 4(2x – 1)

6x ≥ 3 + 8x - 4

6x - 8x ≥ -1

-2x ≥ -1

x ≤ 1/2

or 1 ≥ 2x.

Answer 2

6x ≥ 3 + 4(2x - 1)

⇔ 6x ≥ 3 + 8x - 4 => remove the parentheses

⇔ 6x - 8x ≥ 3 - 4

⇔ -2x ≥ -1

⇔ 2x ≤ 1 (or 1 ≥ 2x)

⇔ x ≤ 1/2

⇔ x ≤ 0.5

The answer for the question should be:

1 ≥ 2x

6x ≥ 3 + 8x – 4

and the first graph.