Writing and Solving Two-Step Inequalities

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40
• 1.50x + 10 ≤ 40
• 1.50x + 10 <40
• 10x + 1.50 < 40

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve -10 - 5x ≥ 25

• x ≤ 3
• x ≥ -7
• x  ≤ -7
• x ≥ -3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

The temperature in the ice rink must stay below 50°F. This morning, the temperature was 71°F. The ice rink runs a cooling device that can decrease the temperature by 3.5° every hour. Which inequality shows how long it will take for the temperature to fall below 50°F?

• 50 + 3.5x < 71
• 71 - 3.5x < 50
• 71 - 3.5x ≤ 50
• 71 + 3.5x < 50

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve -2x - 8 ≤ 18

• x ≤ -13
• x ≤ 5
• x ≥ -5
• x ≥ -13

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 200 + 25x ≥ 500
• 500 + 25x ≥ 200
• 500 - 25x ≥ 200
• 500 - 25x ≤ 200

Tags

CCSS.7.EE.B.4B

The members of Carver Middle School's Junior Beta Club need to raise at least $2000 to attend their national convention. They raised $300 with their last fundraiser and decide to host a school talent show to raise the rest. They plan to charge $10 for each ticket. Which inequality shows the number of tickets they must sale to reach their goal?

• 300x + 10 ≥ 2000
• 10x + 300 ≤ 2000
• 10x + 300 > 2000
• 300 + 10x ≥ 2000

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

Solve 8 + 4x > 24

• x > 4
• x > 8
• x > 64
• x < 8

Tags

CCSS.7.EE.B.4B

The vet told Casey that her dog should weigh at most 70 lbs. Her dog weighs 106 pounds, so Casey set a goal that he would lose 4 pounds per week. Which inequality represents the number of weeks it take for Casey's dog to reach 70 lbs?

• 106 - 4x ≤ 70
• 70 + 4x ≤ 106
• 4x - 106 ≥ 70
• 106 - 4x< 70

Tags

CCSS.7.EE.B.4B