Alg 1 Day 3 Solving Multistep Inequalities

Do I need to flip my inequality symbol?
-3x  ≥ 12

• Yes, because I'll be dividing by a negative number (-3)

• No, because I am dividing a positive number 12

Answer explanation

Yes, you need to flip the inequality symbol when dividing by a negative number. In this case, dividing both sides of -3x ≥ 12 by -3 requires flipping the symbol to get x ≤ -4.

Tags

CCSS.6.EE.B.8

Do I need to flip my inequality symbol?
3x  ≥ -12

• Yes, because I'll be dividing by a negative number

• No, because you I am dividing by a positive

Answer explanation

No, because I am dividing by a positive number. When you divide or multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.

Tags

CCSS.6.EE.B.8

2x + 6 ≥ -8

• x ≥ -7

• x ≤ -7

• x ≥ -10 

• x ≤ -10

Answer explanation

To solve 2x + 6 ≥ -8, subtract 6 from both sides: 2x ≥ -14. Then, divide by 2: x ≥ -7. Thus, the correct answer is x ≥ -7.

Tags

CCSS.7.EE.B.4B

-3x − 4 < 5

• x > -3

• x < -3

• x < 3

• x > 3

Answer explanation

To solve -3x - 4 < 5, add 4 to both sides: -3x < 9. Then, divide by -3 (remember to flip the inequality): x > -3. Thus, the correct answer is x > -3.

Tags

CCSS.7.EE.B.4B

Solve

5x - 7 ≥ 8

• x > 3

• x ≤ ⅕

• x ≥ 3

• x ≤ ⅕

Answer explanation

To solve 5x - 7 ≥ 8, add 7 to both sides: 5x ≥ 15. Then, divide by 5: x ≥ 3. Thus, the correct answer is x ≥ 3.

Tags

CCSS.7.EE.B.4B

-9x + 7 ≥ 25

• x ≥ -3.6

• x ≤ 2

• x ≥ -2

• x ≤ -2

Answer explanation

To solve -9x + 7 ≥ 25, subtract 7 from both sides to get -9x ≥ 18. Dividing by -9 reverses the inequality, yielding x ≤ -2. Thus, the correct answer is x ≤ -2.

Tags

CCSS.7.EE.B.4B

• x > 20

• x ≥ 4

• x ≥ 5

• x ≥ 20

• x ≥ -20

Tags

CCSS.7.EE.B.4B

• x ≤ 20

• x ≥ 4

• x ≥ -20

• x ≥ 20

• x ≤ -20

Tags

CCSS.7.EE.B.4B

Answer explanation

To solve the inequality 2x + 5 + 3x < 10, combine like terms to get 5x + 5 < 10. Subtract 5 from both sides to obtain 5x < 5, then divide by 5 to find x < 1. Thus, the correct answer is x < 1.

6(n + 2) < -72

• n < -14

• n < 35/3

• n < -10

• ∞

Answer explanation

To solve 6(n + 2) < -72, first divide by 6: n + 2 < -12. Then, subtract 2: n < -14. Thus, the correct answer is n < -14.

Tags

CCSS.7.EE.B.4B