7th Grade Math · Unit 4
Reverse the inequality symbol when you multiply or divide by a negative number.
Reverse the symbol
Multiplying or dividing both sides by a negative number reverses the inequality symbol.
Greater than becomes less than, and ≤ becomes ≥. The other direction changes too.
Adding does not flip
Adding or subtracting the same number does not reverse the symbol.
Flip only when the number you multiply or divide by is negative.
Undo in order
Undo addition or subtraction first.
Then divide by the negative coefficient, or multiply by its reciprocal, and reverse the symbol.
One step. Dividing by a negative number reverses the symbol.
−2x > 8
Divide both sides by −2. The inequality symbol reverses.
x < −4
Answer: x < −4
−3x < 9
Divide both sides by −3. The inequality symbol reverses.
x > −3
Answer: x > −3
−4x > 12
Divide both sides by −4. The inequality symbol reverses.
x < −3
Answer: x < −3
−2x ≤ 6
Divide both sides by −2. The inequality symbol reverses.
x ≥ −3
Answer: x ≥ −3
−5x ≥ 20
Divide both sides by −5. The inequality symbol reverses.
x ≤ −4
Answer: x ≤ −4
−6x < 18
Divide both sides by −6. The inequality symbol reverses.
x > −3
Answer: x > −3
−3x > 15
Divide both sides by −3. The inequality symbol reverses.
x < −5
Answer: x < −5
−4x ≤ 8
Divide both sides by −4. The inequality symbol reverses.
x ≥ −2
Answer: x ≥ −2
−2x ≥ 10
Divide both sides by −2. The inequality symbol reverses.
x ≤ −5
Answer: x ≤ −5
−5x < 10
Divide both sides by −5. The inequality symbol reverses.
x > −2
Answer: x > −2
−8x > 16
Divide both sides by −8. The inequality symbol reverses.
x < −2
Answer: x < −2
Undo addition or subtraction first. Then reverse the symbol.
−4x + 2 > 10
−4x + 2 − 2 > 10 − 2
−4x > 8
Divide both sides by −4. The inequality symbol reverses.
x < −2
Answer: x < −2
−2x + 4 > 10
−2x + 4 − 4 > 10 − 4
−2x > 6
Divide both sides by −2. The inequality symbol reverses.
x < −3
Answer: x < −3
−3x + 6 < 0
−3x + 6 − 6 < 0 − 6
−3x < −6
Divide both sides by −3. The inequality symbol reverses.
x > 2
Answer: x > 2
−4x + 8 ≤ 0
−4x + 8 − 8 ≤ 0 − 8
−4x ≤ −8
Divide both sides by −4. The inequality symbol reverses.
x ≥ 2
Answer: x ≥ 2
−2x + 10 ≥ 4
−2x + 10 − 10 ≥ 4 − 10
−2x ≥ −6
Divide both sides by −2. The inequality symbol reverses.
x ≤ 3
Answer: x ≤ 3
−5x + 15 > 5
−5x + 15 − 15 > 5 − 15
−5x > −10
Divide both sides by −5. The inequality symbol reverses.
x < 2
Answer: x < 2
−3x + 9 < 3
−3x + 9 − 9 < 3 − 9
−3x < −6
Divide both sides by −3. The inequality symbol reverses.
x > 2
Answer: x > 2
−4x + 12 ≤ 4
−4x + 12 − 12 ≤ 4 − 12
−4x ≤ −8
Divide both sides by −4. The inequality symbol reverses.
x ≥ 2
Answer: x ≥ 2
−2x + 3 ≥ 9
−2x + 3 − 3 ≥ 9 − 3
−2x ≥ 6
Divide both sides by −2. The inequality symbol reverses.
x ≤ −3
Answer: x ≤ −3
−6x + 6 > 18
−6x + 6 − 6 > 18 − 6
−6x > 12
Divide both sides by −6. The inequality symbol reverses.
x < −2
Answer: x < −2
−3x + 5 < −1
−3x + 5 − 5 < −1 − 5
−3x < −6
Divide both sides by −3. The inequality symbol reverses.
x > 2
Answer: x > 2
The coefficient is a negative fraction.
−32x + 9 > 3
−32x + 9 − 9 > 3 − 9
−32x > −6
Divide both sides by −32. The inequality symbol reverses.
x < 4
Answer: x < 4
−32x + 6 > 0
−32x + 6 − 6 > 0 − 6
−32x > −6
Divide both sides by −32. The inequality symbol reverses.
x < 4
Answer: x < 4
−14x + 2 < 0
−14x + 2 − 2 < 0 − 2
−14x < −2
Divide both sides by −14. The inequality symbol reverses.
x > 8
Answer: x > 8
−12x + 5 ≤ 1
−12x + 5 − 5 ≤ 1 − 5
−12x ≤ −4
Divide both sides by −12. The inequality symbol reverses.
x ≥ 8
Answer: x ≥ 8
−23x + 4 ≥ 0
−23x + 4 − 4 ≥ 0 − 4
−23x ≥ −4
Divide both sides by −23. The inequality symbol reverses.
x ≤ 6
Answer: x ≤ 6
−34x + 3 > 0
−34x + 3 − 3 > 0 − 3
−34x > −3
Divide both sides by −34. The inequality symbol reverses.
x < 4
Answer: x < 4
−25x + 4 < 2
−25x + 4 − 4 < 2 − 4
−25x < −2
Divide both sides by −25. The inequality symbol reverses.
x > 5
Answer: x > 5
−43x + 8 ≤ 0
−43x + 8 − 8 ≤ 0 − 8
−43x ≤ −8
Divide both sides by −43. The inequality symbol reverses.
x ≥ 6
Answer: x ≥ 6
−52x + 10 ≥ 0
−52x + 10 − 10 ≥ 0 − 10
−52x ≥ −10
Divide both sides by −52. The inequality symbol reverses.
x ≤ 4
Answer: x ≤ 4
−35x + 6 > 3
−35x + 6 − 6 > 3 − 6
−35x > −3
Divide both sides by −35. The inequality symbol reverses.
x < 5
Answer: x < 5
−13x + 4 < 1
−13x + 4 − 4 < 1 − 4
−13x < −3
Divide both sides by −13. The inequality symbol reverses.
x > 9
Answer: x > 9
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