Question

Which values from the set {−6, −4, −2, 0, 2, 4, 6} satisfy this inequality?

3 + 1/2 x ≥ 4

answers:

–6, –4, –2 and 0 only

0, 2 and 4 only

2, 4 and 6 only

–4, –2 and 0 only

Answer 1

To find the values that satisfy the inequality, we can substitute each value from the set into the inequality and test if the inequality is true.

Substituting -6 into the inequality, we have:

3 + 1/2(-6) ≥ 4
3 - 3 ≥ 4
0 ≥ 4

The inequality is not true when x = -6.

Substituting -4 into the inequality, we have:

3 + 1/2(-4) ≥ 4
3 - 2 ≥ 4
1 ≥ 4

The inequality is not true when x = -4.

Substituting -2 into the inequality, we have:

3 + 1/2(-2) ≥ 4
3 - 1 ≥ 4
2 ≥ 4

The inequality is not true when x = -2.

Substituting 0 into the inequality, we have:

3 + 1/2(0) ≥ 4
3 + 0 ≥ 4
3 ≥ 4

The inequality is not true when x = 0.

Substituting 2 into the inequality, we have:

3 + 1/2(2) ≥ 4
3 + 1 ≥ 4
4 ≥ 4

The inequality is true when x = 2.

Substituting 4 into the inequality, we have:

3 + 1/2(4) ≥ 4
3 + 2 ≥ 4
5 ≥ 4

The inequality is true when x = 4.

Substituting 6 into the inequality, we have:

3 + 1/2(6) ≥ 4
3 + 3 ≥ 4
6 ≥ 4

The inequality is true when x = 6.

From our calculations, we can see that the values 2, 4, and 6 satisfy the inequality. Therefore, the correct answer is:

2, 4 and 6 only