Solve the absolute value inequality |3x - 2| ≤ 4. What is the range of x?

To solve the absolute value inequality |3x - 2| ≤ 4, we start by breaking down what the inequality means. The expression |3x - 2| ≤ 4 tells us that the distance of 3x - 2 from 0 is at most 4. This leads us to the two inequalities:

1. 3x - 2 ≤ 4

2. 3x - 2 ≥ -4

We will solve each of these inequalities separately.

For the first inequality, 3x - 2 ≤ 4:

Adding 2 to both sides gives:

3x ≤ 6

Dividing both sides by 3 results in:

x ≤ 2

Now, for the second inequality, 3x - 2 ≥ -4:

Adding 2 to both sides gives:

3x ≥ -2

Dividing both sides by 3 results in:

x ≥ -2/3

Combining both results, we find the range of x must satisfy both conditions:

-2/3 ≤ x ≤ 2

Thus, the correct answer provides the range of x that satisfies the original absolute value inequality, indicating that values of x are bounded between -2/3 and