Would You Rather: Simple Inequalities

Would you rather have x + 4 < 12 dollars or x - 3 > 5 dollars?

• x - 3 < 5 dollars
• x + 4 < 12 dollars

Answer explanation

Choose x + 4 < 12 dollars. Solving gives x < 8, meaning you can have up to 8 dollars. For x - 3 > 5, solving gives x > 8, which means you need more than 8 dollars. The first option is better.

Would you rather spend 2x < 18 minutes on homework or x + 6 <= 20 minutes?

• x + 6 > 20 minutes
• 2x < 18 minutes

Answer explanation

To solve 2x < 18, x < 9. For x + 6 <= 20, x <= 14. Since x < 9 is more restrictive, choose 2x < 18 minutes for less homework time.

Would you rather earn 3x > 15 per hour or x + 2 < 10 per hour?

• 3x > 15 is better than x + 2 < 10.
• x + 2 > 10 is better than 3x < 15.

Answer explanation

To solve 3x > 15, x > 5, meaning you earn more than $15/hour. For x + 2 < 10, x < 8, meaning you earn less than $8/hour. Earning 3x > 15 is the better choice as it offers a higher potential income.

Would you rather solve x - 5 < 8 problems or 2x + 3 > 13 problems?

• 2x + 3 < 13 problems
• x - 5 < 8 problems

Answer explanation

To solve x - 5 < 8, we get x < 13. For 2x + 3 > 13, we find x > 5. The first inequality has a broader range (x < 13) compared to the second (x > 5). Thus, solving x - 5 < 8 problems is preferable.

Would you rather get x >= 70 on a test or x < 90?

• Get x >= 70 on a test

• Get x < 90

Answer explanation

Choosing 'x >= 70' ensures a passing score, while 'x < 90' does not guarantee a passing grade. Therefore, 'Get x >= 70 on a test' is the better choice for achieving a minimum acceptable performance.

Would you rather have x > -2 siblings or x < 5 pets?

• x < 5 pets
• x >-2

Answer explanation

Choosing x < 5 pets is preferable as it allows for a maximum of 4 pets, which is manageable and can provide companionship. In contrast, x > -2 siblings could mean having many siblings, which might be overwhelming.

Would you rather walk x + 3 < 10 miles or 2x - 4 > 6 miles?

• 2x - 4 > 6 miles
• x + 3 < 10 miles

Answer explanation

To solve x + 3 < 10, we get x < 7, meaning you walk less than 7 miles. For 2x - 4 > 6, we find x > 5, meaning you walk more than 5 miles. Walking less than 7 miles is preferable, so choose x + 3 < 10.

Would you rather have x <= 100 followers or x > 50 likes?

• x > 50 likes
• x <=100 followers

Answer explanation

Choosing x > 50 likes is preferable as it indicates higher engagement and appreciation for your content, while having x <= 100 followers does not guarantee interaction or interest.

Would you rather read x - 2 < 5 chapters or x + 1 > 6 chapters?

• x + 1 > 6 chapters
• x - 2 < 5 chapters

Answer explanation

To solve x - 2 < 5, we get x < 7, meaning less than 7 chapters. For x + 1 > 6, we find x > 5, meaning more than 5 chapters. Thus, reading x - 2 < 5 chapters (less than 7) is the better choice.

Would you rather have x < 20 minutes of screen time or x > 10 minutes of reading?

• x < 20 minutes of screen time

• x > 10 minutes of reading

Answer explanation

Choosing x > 10 minutes of reading is preferable as it promotes learning and cognitive engagement, while x < 20 minutes of screen time may lead to passive consumption and less intellectual stimulation.