Let’s solve each inequality one by one. We’ll isolate the variable on one side, just like solving equations — but remember: if you multiply or divide by a negative number, flip the inequality sign! (None of these require flipping, though.)
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1. 7w ≤ 42
Divide both sides by 7:
→ w ≤ 6
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2. k/4 ≤ -4
Multiply both sides by 4:
→ k ≤ -16
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3. -5 > p/8
Multiply both sides by 8:
→ -40 > p
Which is the same as:
→ p < -40
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4. 15 < r + 14
Subtract 14 from both sides:
→ 1 < r
Or:
→ r > 1
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5. 3k ≥ -24
Divide both sides by 3:
→ k ≥ -8
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6. -6 ≥ m/4
Multiply both sides by 4:
→ -24 ≥ m
Or:
→ m ≤ -24
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7. t/6 < -3
Multiply both sides by 6:
→ t < -18
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8. -5 < (1/3)t
Multiply both sides by 3:
→ -15 < t
Or:
→ t > -15
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9. -6 < s - 11
Add 11 to both sides:
→ 5 < s
Or:
→ s > 5
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10. x + 14 ≥ -5
Subtract 14 from both sides:
→ x ≥ -19
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Final Answer:
w ≤ 6
k ≤ -16
p < -40
r > 1
k ≥ -8
m ≤ -24
t < -18
t > -15
s > 5
x ≥ -19
Parent Tip: Review the logic above to help your child master the concept of inequalities equations worksheet.
