How many integral values of x satisfy the inequality |3x – 5| ≤ 15?

To solve the inequality |3x – 5| ≤ 15, we need to break it down into two separate inequalities because of the absolute value.

1. The first inequality is 3x - 5 ≤ 15. To solve for x, we first add 5 to both sides to get 3x ≤ 20. Then, we divide both sides by 3 to get x ≤ 20/3. The integral values of x that satisfy this inequality are x = -1, 0, 1, 2, 3, 4, 5, 6.

2. The second inequality is -(3x - 5) ≤ 15. This simplifies to -3x + 5 ≤ 15. We then subtract 5 from both sides to get -3x ≤ 10. Finally, we divide both sides by -3 (remembering to flip the inequality sign) to get x ≥ -10/3. The integral values of x that satisfy this inequality are x = -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.

Therefore, the integral values of x that satisfy the original inequality |3x – 5| ≤ 15 are x = -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. So, there are 10 integral values of x that satisfy the inequality.