Solve the given inequalities on this printable worksheet.

Here are the step-by-step solutions for each inequality on the worksheet.

1) $3x - 8 \le 22$
* Add 8 to both sides: $3x \le 30$
* Divide by 3: $x \le 10$

2) $5r + 10 \ge 19$
* Subtract 10 from both sides: $5r \ge 9$
* Divide by 5: $r \ge \frac{9}{5}$ (or $r \ge 1.8$)

3) $6x - 7 \le 5$
* Add 7 to both sides: $6x \le 12$
* Divide by 6: $x \le 2$

4) $-t + 1 \ge 6$
* Subtract 1 from both sides: $-t \ge 5$
* Divide by -1. Remember: When you divide or multiply by a negative number, flip the inequality sign.
* Result: $t \le -5$

5) $5a - 4 > 2a + 8$
* Subtract $2a$ from both sides: $3a - 4 > 8$
* Add 4 to both sides: $3a > 12$
* Divide by 3: $a > 4$

6) $x + 1 \ge 3x - 18$
* Subtract $x$ from both sides: $1 \ge 2x - 18$
* Add 18 to both sides: $19 \ge 2x$
* Divide by 2: $9.5 \ge x$
* Rewrite with $x$ first: $x \le 9.5$ (or $x \le \frac{19}{2}$)

7) $5x - 2 \ge 68$
* Add 2 to both sides: $5x \ge 70$
* Divide by 5: $x \ge 14$

8) $5(x - 3) \ge 40$
* Divide both sides by 5 first: $x - 3 \ge 8$
* Add 3 to both sides: $x \ge 11$
*(Alternatively, distribute the 5 to get $5x - 15 \ge 40$, add 15 to get $5x \ge 55$, then divide by 5).*

9) $4x + 7 < 11$
* Subtract 7 from both sides: $4x < 4$
* Divide by 4: $x < 1$

10) $4(x - 2) > 20$
* Divide both sides by 4 first: $x - 2 > 5$
* Add 2 to both sides: $x > 7$

11) $4 - 2x \ge -8$
* Subtract 4 from both sides: $-2x \ge -12$
* Divide by -2. Remember: Flip the inequality sign because we are dividing by a negative.
* Result: $x \le 6$

12) $7x - 5 \ge 3x + 11$
* Subtract $3x$ from both sides: $4x - 5 \ge 11$
* Add 5 to both sides: $4x \ge 16$
* Divide by 4: $x \ge 4$

Final Answer:
1) $x \le 10$
2) $r \ge 1.8$
3) $x \le 2$
4) $t \le -5$
5) $a > 4$
6) $x \le 9.5$
7) $x \ge 14$
8) $x \ge 11$
9) $x < 1$
10) $x > 7$
11) $x \le 6$
12) $x \ge 4$