Solving Linear Inequalities (A) worksheet featuring ten problems to solve for the given variables.

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

1. $4 \le 4 + z$
Subtract 4 from both sides:
$4 - 4 \le z$
$0 \le z$
This is the same as saying $z$ is greater than or equal to 0.
Answer: $z \ge 0$

2. $g - 4 \le -8$
Add 4 to both sides:
$g \le -8 + 4$
Answer: $g \le -4$

3. $5 \le -b - 4$
Add 4 to both sides:
$9 \le -b$
Multiply by $-1$. Remember to flip the inequality sign when multiplying by a negative number:
$-9 \ge b$
This is the same as saying $b$ is less than or equal to $-9$.
Answer: $b \le -9$

4. $7 \ge -q + 9$
Subtract 9 from both sides:
$-2 \ge -q$
Multiply by $-1$ and flip the sign:
$2 \le q$
Answer: $q \ge 2$

5. $6 - n \le -5$
Subtract 6 from both sides:
$-n \le -11$
Multiply by $-1$ and flip the sign:
$n \ge 11$
Answer: $n \ge 11$

6. $1 > -a + 3$
Subtract 3 from both sides:
$-2 > -a$
Multiply by $-1$ and flip the sign:
$2 < a$
Answer: $a > 2$

7. $-n + 3 > 6$
Subtract 3 from both sides:
$-n > 3$
Multiply by $-1$ and flip the sign:
$n < -3$
Answer: $n < -3$

8. $-8 - a \ge -5$
Add 8 to both sides:
$-a \ge 3$
Multiply by $-1$ and flip the sign:
$a \le -3$
Answer: $a \le -3$

9. $5 - r < -8$
Subtract 5 from both sides:
$-r < -13$
Multiply by $-1$ and flip the sign:
$r > 13$
Answer: $r > 13$

10. $6 \le -w + 2$
Subtract 2 from both sides:
$4 \le -w$
Multiply by $-1$ and flip the sign:
$-4 \ge w$
This is the same as saying $w$ is less than or equal to $-4$.
Answer: $w \le -4$

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Final Answer:
1. $z \ge 0$
2. $g \le -4$
3. $b \le -9$
4. $q \ge 2$
5. $n \ge 11$
6. $a > 2$
7. $n < -3$
8. $a \le -3$
9. $r > 13$
10. $w \le -4$