Question

In your journal, you made up an inequality and solved it. You also brainstormed what it would look like to communicate your solution clearly if your inequality represented a real-world problem.. In your first post, share your inequality and solution with your peers. Then ask your peers if they can come up with a real-world problem that could be solved using your inequality.

Next, read your peers' inequalities. Respond to two of your peers by providing a unique real-world problem that could be solved with their inequality. Explain what if would look like to communicate the solution to your real-world problem clearly.

Post a detailed response to the Solutions to Real-World Inequality Discussion prompt. Then respond to two classmates' posts.

Participate in the discussion to learn more about writing and solving real-world inequality problems. write it as a 6th grader

Answer 1

Hi everyone — here’s my inequality and how I solved it. I tried to write it like a good math journal so a friend could understand.

My inequality:
3x + 5 < 20

Steps to solve:
1. Subtract 5 from both sides: 3x + 5 − 5 < 20 − 5, so 3x < 15.
2. Divide both sides by 3: (3x)/3 < 15/3, so x < 5.

Answer: x < 5

What this means: x can be any number less than 5 (like 4, 0, −2, or 4.9), but not 5.

Check: If x = 4, then 3(4) + 5 = 12 + 5 = 17, and 17 < 20 is true.
If x = 5, then 3(5) + 5 = 20, but 20 < 20 is false. So 5 is not allowed.

Question for you: Can you think of a real-world problem that could be solved using x < 5? Try to make it interesting (like how many cookies, how long you can play, or how many friends can come). Also tell how you would explain the solution clearly to someone else.

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Reply to Peer 1 (inequality they posted: 2n + 4 ≥ 12)

Restating and solving quickly:
2n + 4 ≥ 12
Subtract 4: 2n ≥ 8
Divide 2: n ≥ 4

Real-world problem that fits: A classroom needs at least 12 chairs for a group project. Each table has 2 chairs and there are already 4 extra chairs in the room. How many tables (n) should the teacher put in the room so there are at least 12 chairs?

Explanation in simple steps (how I would communicate it):
- Define variable: Let n = number of tables.
- Write inequality: 2n + 4 ≥ 12 (2 chairs per table plus 4 extra chairs must be at least 12).
- Solve step-by-step like above to get n ≥ 4.
- Interpret: The teacher needs 4 or more tables.
- Show a quick check: If n = 4, then 2(4)+4 = 12 chairs, which works.
- Draw a small number line showing the point 4 shaded and an arrow to the right (to show 4 or more).
- Conclude in one sentence: The teacher should use at least 4 tables so each student has a chair.

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Reply to Peer 2 (inequality they posted: 5y − 7 ≤ 18)

Restating and solving quickly:
5y − 7 ≤ 18
Add 7: 5y ≤ 25
Divide 5: y ≤ 5

Real-world problem that fits: A bus ride costs $5 per person minus a $7 coupon applied to the total group cost. The group has at most $18 to spend. How many people (y) can go on the bus?

Explanation in simple steps:
- Define variable: Let y = number of people going.
- Write inequality: 5y − 7 ≤ 18 (total cost is $5 per person minus $7 coupon and must be at most $18).
- Solve to get y ≤ 5.
- Interpret: At most 5 people can go.
- Check with a number: If y = 5, cost = 5(5) − 7 = 25 − 7 = $18, which is okay. If y = 6, cost = 30 − 7 = $23, which is too much.
- Draw a number line with 5 shaded and an arrow to the left (to show 5 or fewer).
- Conclude: No more than 5 people can go with the money available.

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Thanks for reading! I can’t wait to see your real-world ideas for my inequality x < 5.