Solving and Graphing One-Step Inequalities

x − 4 ≤ 6

• x ≤ 10

• x ≥ 10 

• x ≥ 2

• x ≤ 2

Answer explanation

To solve x − 4 ≤ 6, add 4 to both sides: x ≤ 10. Thus, the correct answer is x ≤ 10.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

y − 10 > 14

• y > 24

• y < 24

• y > 4

• y < 4

Answer explanation

To solve y − 10 > 14, add 10 to both sides: y > 24. Thus, the correct answer is y > 24.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

y + 7 ≥ 12

• y ≥ 5

• y ≤ 5 

• y ≥ 19 

• y ≤ 19

Answer explanation

To solve y + 7 ≥ 12, subtract 7 from both sides: y ≥ 12 - 7, which simplifies to y ≥ 5. Thus, the correct answer is y ≥ 5.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

w + 4 ≤ -5

• w ≤ -9 

• w ≥ -9

• w ≤ -1 

• w ≥ -1

Answer explanation

To solve w + 4 ≤ -5, subtract 4 from both sides: w ≤ -5 - 4, which simplifies to w ≤ -9. Thus, the correct answer is w ≤ -9.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

7n > 49

• n > 7

• n < 7

• n > 343

• n < 343

Answer explanation

To solve 7n > 49, divide both sides by 7: n > 7. Thus, the correct answer is n > 7.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

y ⁄ -8 > 2 

• y < -16

• y > -16

• y < -0.25

• y > -0.25

Answer explanation

To solve y / -8 > 2, multiply both sides by -8, reversing the inequality: y < -16. Thus, the correct answer is y < -16.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

k ⁄ -5 < -4

• k > 20

• k < 20 

• k > 0.8 

• k < 0.8

Answer explanation

To solve k / -5 < -4, multiply both sides by -5 (reverse the inequality): k > 20. Thus, the correct answer is k > 20.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

m ⁄ 7 > -14

• m > -98

• m < -98

• m > -2

• m < -2

Answer explanation

To solve m/7 > -14, multiply both sides by 7 (since 7 is positive). This gives m > -98. Thus, the correct answer is m > -98.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

x − 17 > -54

• x > -37

• x < -37

• x > -71

• x < -71

Answer explanation

To solve x − 17 > -54, add 17 to both sides: x > -54 + 17, which simplifies to x > -37. Thus, the correct answer is x > -37.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

26 + y ≤ -18 

• y ≤ -44

• y ≥ -44

• y ≤ 8

• y ≥ 8

Answer explanation

To solve 26 + y ≤ -18, subtract 26 from both sides: y ≤ -18 - 26, which simplifies to y ≤ -44. Thus, the correct answer is y ≤ -44.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3