Two Step Inequality Word Problems Worksheet With Answers - Fill ... - Free Printable
Educational worksheet: Two Step Inequality Word Problems Worksheet With Answers - Fill .... Download and print for classroom or home learning activities.
PNG
298×386
7.5 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #876553
⭐
Show Answer Key & Explanations
Step-by-step solution for: Two Step Inequality Word Problems Worksheet With Answers - Fill ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Two Step Inequality Word Problems Worksheet With Answers - Fill ...
You’ve uploaded a worksheet titled “Writing Two-Step Inequalities” — specifically, Lesson 8.3, Practice and Problem Solving: D.
The task is to:
1. Write an inequality for each given situation (some are done for you).
2. For problems 7–9, write the inequality, solve it, and show your work.
Let’s go through each problem one by one, including solving the ones that require it.
---
> 1. Four times a number is at least 2.
→ 4x ≥ 2 *(Given)*
> 2. One third of the opposite of a number is less than 12.
→ Let the number be *x*. The opposite is *–x*. One third of that is *–x/3*.
So: –x/3 < 12
> 3. A number increased by 5 is less than 7.
→ x + 5 < 7
> 4. Ten less than a number is more than 80.
→ x – 10 > 80
> 5. Two more than 5 times a number is greater than or equal to 17.
→ 5x + 2 ≥ 17
> 6. Six less than two times a number is no more than 11.
→ “No more than” = ≤
→ 2x – 6 ≤ 11
---
---
> 7. An employee of a car wash earns $12 for each car she washes. She always saves $50 of her weekly earnings. This week, she wants to have at least $120 in spending money. What is the fewest number of cars she must wash?
Step 1: Define variable
Let *x* = number of cars washed.
Step 2: Write expression for total earnings
Earnings = 12x
Spending money = Earnings – Savings = 12x – 50
Step 3: Set up inequality
She wants at least $120 in spending money → ≥ 120
→ 12x – 50 ≥ 120
Step 4: Solve
Add 50 to both sides:
→ 12x ≥ 170
Divide by 12:
→ x ≥ 170 / 12
→ x ≥ 14.166...
Since she can’t wash a fraction of a car, and she needs at least $120, she must wash 15 cars (round up).
✔ Answer: She must wash at least 15 cars.
---
> 8. A video game enthusiast saved $750 to spend on a video game player and games. The player costs $400. The games cost $49 each. At most, how many games can she buy with the amount left after buying the player?
Step 1: Define variable
Let *x* = number of games she can buy.
Step 2: Money left after buying player
Total budget: $750
Player cost: $400
Money left for games: 750 – 400 = $350
Each game costs $49 → Total cost for games = 49x
Step 3: Set up inequality
She can spend at most $350 on games → ≤ 350
→ 49x ≤ 350
Step 4: Solve
Divide both sides by 49:
→ x ≤ 350 / 49
→ x ≤ 7.142...
Since she can’t buy a fraction of a game, and “at most” means maximum whole number ≤ 7.14 → x = 7
✔ Answer: She can buy at most 7 games.
---
> 9. A health food producer has 250 samples of a new snack to distribute in the mall. The producer has to keep at least 50 samples for display in the health food store for the product launch. How long will the samples last if consumers are taking the samples at a rate of 20 every hour?
Step 1: Define variable
Let *x* = number of hours the samples will last.
Step 2: Samples available for distribution
Total samples: 250
Must keep 50 for display → Available for distribution: 250 – 50 = 200 samples
Consumers take 20 per hour → Total taken in *x* hours = 20x
Step 3: Set up inequality
Samples taken must be ≤ available samples (so they don’t run out before display is ready)
→ 20x ≤ 200
Step 4: Solve
Divide both sides by 20:
→ x ≤ 10
✔ Answer: The samples will last at most 10 hours.
---
## 📝 Final Answers Summary:
1. 4x ≥ 2
2. –x/3 < 12
3. x + 5 < 7
4. x – 10 > 80
5. 5x + 2 ≥ 17
6. 2x – 6 ≤ 11
---
7.
Inequality: 12x – 50 ≥ 120
Solution: x ≥ 14.166... → x ≥ 15
→ She must wash at least 15 cars.
8.
Inequality: 49x ≤ 350
Solution: x ≤ 7.142... → x ≤ 7
→ She can buy at most 7 games.
9.
Inequality: 20x ≤ 200
Solution: x ≤ 10
→ Samples will last at most 10 hours.
---
✔ All problems solved with explanations! Let me know if you’d like to see the graphs or check your work against this.
The task is to:
1. Write an inequality for each given situation (some are done for you).
2. For problems 7–9, write the inequality, solve it, and show your work.
Let’s go through each problem one by one, including solving the ones that require it.
---
✔ Problems 1–6: Write an inequality (already partially filled)
> 1. Four times a number is at least 2.
→ 4x ≥ 2 *(Given)*
> 2. One third of the opposite of a number is less than 12.
→ Let the number be *x*. The opposite is *–x*. One third of that is *–x/3*.
So: –x/3 < 12
> 3. A number increased by 5 is less than 7.
→ x + 5 < 7
> 4. Ten less than a number is more than 80.
→ x – 10 > 80
> 5. Two more than 5 times a number is greater than or equal to 17.
→ 5x + 2 ≥ 17
> 6. Six less than two times a number is no more than 11.
→ “No more than” = ≤
→ 2x – 6 ≤ 11
---
✍️ Problems 7–9: Write AND solve the inequality
---
> 7. An employee of a car wash earns $12 for each car she washes. She always saves $50 of her weekly earnings. This week, she wants to have at least $120 in spending money. What is the fewest number of cars she must wash?
Step 1: Define variable
Let *x* = number of cars washed.
Step 2: Write expression for total earnings
Earnings = 12x
Spending money = Earnings – Savings = 12x – 50
Step 3: Set up inequality
She wants at least $120 in spending money → ≥ 120
→ 12x – 50 ≥ 120
Step 4: Solve
Add 50 to both sides:
→ 12x ≥ 170
Divide by 12:
→ x ≥ 170 / 12
→ x ≥ 14.166...
Since she can’t wash a fraction of a car, and she needs at least $120, she must wash 15 cars (round up).
✔ Answer: She must wash at least 15 cars.
---
> 8. A video game enthusiast saved $750 to spend on a video game player and games. The player costs $400. The games cost $49 each. At most, how many games can she buy with the amount left after buying the player?
Step 1: Define variable
Let *x* = number of games she can buy.
Step 2: Money left after buying player
Total budget: $750
Player cost: $400
Money left for games: 750 – 400 = $350
Each game costs $49 → Total cost for games = 49x
Step 3: Set up inequality
She can spend at most $350 on games → ≤ 350
→ 49x ≤ 350
Step 4: Solve
Divide both sides by 49:
→ x ≤ 350 / 49
→ x ≤ 7.142...
Since she can’t buy a fraction of a game, and “at most” means maximum whole number ≤ 7.14 → x = 7
✔ Answer: She can buy at most 7 games.
---
> 9. A health food producer has 250 samples of a new snack to distribute in the mall. The producer has to keep at least 50 samples for display in the health food store for the product launch. How long will the samples last if consumers are taking the samples at a rate of 20 every hour?
Step 1: Define variable
Let *x* = number of hours the samples will last.
Step 2: Samples available for distribution
Total samples: 250
Must keep 50 for display → Available for distribution: 250 – 50 = 200 samples
Consumers take 20 per hour → Total taken in *x* hours = 20x
Step 3: Set up inequality
Samples taken must be ≤ available samples (so they don’t run out before display is ready)
→ 20x ≤ 200
Step 4: Solve
Divide both sides by 20:
→ x ≤ 10
✔ Answer: The samples will last at most 10 hours.
---
## 📝 Final Answers Summary:
Problems 1–6 (Inequalities only):
1. 4x ≥ 2
2. –x/3 < 12
3. x + 5 < 7
4. x – 10 > 80
5. 5x + 2 ≥ 17
6. 2x – 6 ≤ 11
---
Problems 7–9 (Write & Solve):
7.
Inequality: 12x – 50 ≥ 120
Solution: x ≥ 14.166... → x ≥ 15
→ She must wash at least 15 cars.
8.
Inequality: 49x ≤ 350
Solution: x ≤ 7.142... → x ≤ 7
→ She can buy at most 7 games.
9.
Inequality: 20x ≤ 200
Solution: x ≤ 10
→ Samples will last at most 10 hours.
---
✔ All problems solved with explanations! Let me know if you’d like to see the graphs or check your work against this.
Parent Tip: Review the logic above to help your child master the concept of two step inequalities word problems worksheet.
