Question

Which of the following values are solutions to the inequality 4 ≤ 6x > 2?

i. -2
ii. -6
iii. -1
iv. 3

a. i and ii
b. ii and iii
c. i and iii
d. iii and iv

Answer 1

To solve the inequality 4 ≤ 6x > 2, divide it into two separate inequalities: 4 ≤ 6x and 6x > 2. Solve each inequality individually and combine the solutions. Check which given values satisfy the resulting inequalities. The values that satisfy the inequality are -1 and 3.

Step-by-step explanation:

To solve the inequality 4 ≤ 6x > 2, we need to break it down into two separate inequalities:

4 ≤ 6x

6x > 2

We solve each inequality individually:

4 ≤ 6x:

Divide both sides by 6: 4/6 ≤ x

Simplify: 2/3 ≤ x

6x > 2:

Divide both sides by 6: x > 2/6

Simplify: x > 1/3

Combining the two solutions, we have 2/3 ≤ x and x > 1/3.

Now we check which values from the given options satisfy these inequalities:

i. -2: -2 does not satisfy 2/3 ≤ x.

ii. -6: -6 does not satisfy 2/3 ≤ x.

iii. -1: -1 satisfies both 2/3 ≤ x and x > 1/3.

iv. 3: 3 satisfies both 2/3 ≤ x and x > 1/3.

Therefore, the values that are solutions to the inequality are iii. -1 and iv. 3.

Answer 2

To find the values that are solutions to the inequality 4 ≤ 6x > 2, we need to solve two separate inequalities. The solutions are x ≥ 2/3 and x > 1/3. The values that satisfy both inequalities are i. and iii., so the correct answer is c. i and iii.

Step-by-step explanation:

To find the values that are solutions to the inequality 4 ≤ 6x > 2, we need to solve two separate inequalities. First, we solve the inequality 4 ≤ 6x:

1. Divide both sides by 6: 4/6 ≤ x
2. Simplify: 2/3 ≤ x

So, x ≥ 2/3.

Next, we solve the inequality 6x > 2:

1. Divide both sides by 6: x > 2/6 or x > 1/3

So, x > 1/3.

Therefore, the values that satisfy both inequalities are x ≥ 2/3 and x > 1/3. The only option that includes both i. and iii. is c. i and iii.