Solve Linear Inequalities worksheet featuring eight algebraic problems to practice solving inequalities.

Let's solve each of the linear inequalities step by step.

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1. $ 7w \leq 42 $

Step: Divide both sides by 7
$$
w \leq \frac{42}{7} = 6
$$

✔ Solution: $ w \leq 6 $

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2. $ \frac{k}{4} \leq -4 $

Step: Multiply both sides by 4
$$
k \leq -4 \times 4 = -16
$$

✔ Solution: $ k \leq -16 $

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3. $ -5 > \frac{p}{8} $

Step: Multiply both sides by 8
$$
-5 \times 8 > p \Rightarrow -40 > p
$$
or equivalently:
$$
p < -40
$$

✔ Solution: $ p < -40 $

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4. $ 15 < r + 14 $

Step: Subtract 14 from both sides
$$
15 - 14 < r \Rightarrow 1 < r
$$
or:
$$
r > 1
$$

✔ Solution: $ r > 1 $

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5. $ 3k \geq -24 $

Step: Divide both sides by 3
$$
k \geq \frac{-24}{3} = -8
$$

✔ Solution: $ k \geq -8 $

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6. $ -6 \geq \frac{m}{4} $

Step: Multiply both sides by 4
$$
-6 \times 4 \geq m \Rightarrow -24 \geq m
$$
or:
$$
m \leq -24
$$

✔ Solution: $ m \leq -24 $

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7. $ \frac{t}{6} < -3 $

Step: Multiply both sides by 6
$$
t < -3 \times 6 = -18
$$

✔ Solution: $ t < -18 $

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8. $ -5 < \frac{1}{3}t $

Step: Multiply both sides by 3
$$
-5 \times 3 < t \Rightarrow -15 < t
$$
or:
$$
t > -15
$$

✔ Solution: $ t > -15 $

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9. $ -6 < s - 11 $

Step: Add 11 to both sides
$$
-6 + 11 < s \Rightarrow 5 < s
$$
or:
$$
s > 5
$$

✔ Solution: $ s > 5 $

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10. $ x + 14 \geq -5 $

Step: Subtract 14 from both sides
$$
x \geq -5 - 14 = -19
$$

✔ Solution: $ x \geq -19 $

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✔ Final Answers:

1. $ w \leq 6 $
2. $ k \leq -16 $
3. $ p < -40 $
4. $ r > 1 $
5. $ k \geq -8 $
6. $ m \leq -24 $
7. $ t < -18 $
8. $ t > -15 $
9. $ s > 5 $
10. $ x \geq -19 $

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Let me know if you'd like these graphed on a number line or written in interval notation!