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The solution to the inequality |3x - 2| ≤ 5 is -1 ≤ x ≤ 7/3.

To solve this inequality, we need to consider two cases: when 3x - 2 is positive and when it is negative.

Case 1: 3x - 2 ≥ 0

In this case, the inequality becomes 3x - 2 ≤ 5, which simplifies to 3x ≤ 7. Dividing both sides by 3, we get x ≤ 7/3.

Case 2: 3x - 2 < 0

In this case, the inequality becomes -(3x - 2) ≤ 5, which simplifies to -3x + 2 ≤ 5. Subtracting 2 from both sides, we get -3x ≤ 3. Dividing both sides by -3 and flipping the inequality, we get x ≥ -1.

Therefore, the solution to the inequality is -1 ≤ x ≤ 7/3. We can check this by plugging in values within this range and verifying that they satisfy the inequality. For example, when x = 0, |3x - 2| = 2, which is less than or equal to 5. When x = 2, |3x - 2| = 4, which is also less than or equal to 5.

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