Question

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Select three options.

1 ≥ 2x
6x ≥ 3 + 8x – 4
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at negative 0.5 and a bold line starts at negative 0.5 and is pointing to the right.
A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the right.

Answer 1

Solve: 6x ≥ 3 + 4(2x − 1) → 6x ≥ 3 + 8x − 4 = 8x − 1 → −2x ≥ −1 → 2x ≤ 1 → x ≤ 1/2.

So the three correct representations are:
- 1 ≥ 2x (equivalent to 2x ≤ 1)
- 6x ≥ 3 + 8x − 4 (algebraic expansion of the original)
- the number line with a filled point at 0.5 and the bold line/arrow pointing left (represents x ≤ 0.5).

The other number-line options represent x ≥ −0.5 or x ≥ 0.5, which are not correct.