Inequality Word Problems Lesson Plans & Worksheets - Free Printable

It looks like you've uploaded a document containing a set of word problems related to linear equations, specifically focusing on setting up and solving equations using algebra. However, since I can't view images directly, I’ll need you to either:

1. Type out the text of the problems from the image, or
2. Describe the content of the image so I can help solve it.

But based on your message, I see that the text is already partially visible in your query — here are the problems as they appear:

---

Algebra 1

Open-ended/Inequality Word Problems

1) Chris has a total of $50. He spends $30 at the school store. How much money does he have left?
a) Write an equation to represent the situation. Be sure to define your variable.
b) Solve the inequality to find the maximum number of students in her class.

> Wait — this seems inconsistent. The first part is about money, but the second refers to "students in her class." This might be a formatting error.

Let me go through each problem carefully and solve them one by one assuming the correct context based on typical word problems.

---

Problem 1:

> Chris has a total of $50. He spends $30 at the school store. How much money does he have left?

#### a) Write an equation to represent the situation.
Let \( x \) = amount of money Chris has left.

He started with $50 and spent $30, so:
\[
x = 50 - 30
\]

Or more generally:
\[
x = 50 - 30
\Rightarrow x = 20
\]

So, Chris has $20 left.

#### b) Solve the inequality to find the maximum number of students in her class.

Wait — this doesn’t make sense in context. There’s no mention of students in this problem. This appears to be a mistake in the problem statement — likely the second part (b) belongs to a different problem.

Let’s assume that Problem 1 only asks for the equation and solution for the money.

✔ Answer:
- Equation: \( x = 50 - 30 \)
- Solution: \( x = 20 \)

Chris has $20 left.

---

Problem 2:

> Miss Jones had 450 students come to her club. Then, there were 180 added, and some students decided to leave.

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality to find the minimum number of people in the club.

We’re missing information — how many left? But let's suppose the intent is:

> “Then, there were 180 added, and some students decided to leave.”
> Suppose we want to know how many could have left such that at least 300 remain?

But again, it's unclear.

Alternatively, maybe it's:
"Miss Jones had 450 students. Then 180 joined, and some left. Now she has at least 400 students."

That would make sense.

Let’s assume:
- Initial: 450
- Added: 180 → Total before leaving: \( 450 + 180 = 630 \)
- Let \( x \) = number who left
- After leaving: \( 630 - x \)
- We are told that at least 400 remain, so:
\[
630 - x \geq 400
\]

Now solve:
\[
630 - x \geq 400 \\
-x \geq 400 - 630 \\
-x \geq -230 \\
x \leq 230
\]

So, no more than 230 students left.

But the question says: find the minimum number of people in the club.

If we want the minimum possible number, then we’d need to minimize \( 630 - x \), which happens when \( x \) is maximized.

But if \( x \leq 230 \), then the minimum number remaining is:
\[
630 - 230 = 400
\]

So the minimum number in the club is 400.

But the problem says: “solve the inequality to find the minimum number of people.”

So perhaps the intended answer is 400.

✔ Assuming the condition is "at least 400 remain":

a) Let \( x \) = number of students who left
Equation:
\[
630 - x \geq 400
\]

b) Solving:
\[
x \leq 230
\]
So the minimum number of people in the club is 400.

---

Problem 3:

> Bill spent less than $85 on a magazine and five compact discs. The magazine cost $4.

a) Write an inequality to represent the situation. Be sure to define your variable.

Let \( x \) = cost of one compact disc.

He bought 5 CDs and 1 magazine ($4), total < $85:
\[
5x + 4 < 85
\]

b) Solve the inequality to find the maximum number of CDs he could buy.

Wait — he already bought 5 CDs. So the question may be asking: what is the maximum price per CD such that total < $85?

But it says: “maximum number of CDs” — but it says he bought five.

This is confusing.

Wait — maybe the problem is:
> Bill spent less than $85 on a magazine and some compact discs. The magazine cost $4. Each CD costs $12.

Then: Let \( x \) = number of CDs.

Total cost:
\[
4 + 12x < 85
\]

Then solve:
\[
12x < 81 \\
x < 6.75
\]

So maximum whole number of CDs is 6.

But the original says: “five compact discs”.

Let’s re-read:

> Bill spent less than $85 on a magazine and five compact discs. The magazine cost $4.

So he bought exactly 5 CDs.

Then:
\[
\text{Cost} = 4 + 5x < 85 \\
5x < 81 \\
x < 16.2
\]

So the maximum cost per CD is $16.19, but not the number.

But the question says: “find the maximum number of CDs he could buy”

Contradiction.

Possibility: Maybe it was supposed to say:
> Bill spent less than $85 on a magazine and some compact discs. The magazine cost $4. Each CD costs $12.

Then:
\[
4 + 12x < 85 \\
12x < 81 \\
x < 6.75
\Rightarrow x \leq 6
\]

So maximum number of CDs is 6.

I think this is the intended version.

So let’s assume:

> Bill spent less than $85 on a magazine and some compact discs. The magazine cost $4. Each CD costs $12.

a) Let \( x \) = number of CDs
\[
4 + 12x < 85
\]

b) Solve:
\[
12x < 81 \\
x < 6.75
\Rightarrow x \leq 6
\]

So maximum number of CDs = 6

✔ Answer:
a) \( 4 + 12x < 85 \)
b) Maximum number of CDs = 6

---

Problem 4:

> A standard ticket costs $20. Some students get a discount. They charged her $12 per ticket. She paid $180.

a) Write an inequality to represent the situation. Be sure to define your variable.

Let \( x \) = number of tickets she bought.

Each ticket is $12 (discounted), total paid: $180

So:
\[
12x = 180
\]

But it says “inequality”? That suggests something like “she paid less than $180” or “up to $180”.

But it says: “She paid $180” — so equality.

Maybe: “She paid no more than $180”?

Let’s suppose:
> She paid no more than $180.

Then:
\[
12x \leq 180
\]

Then solve:
\[
x \leq 15
\]

So maximum number of tickets = 15.

But the problem says: “She paid $180”, so likely:
\[
12x = 180 \Rightarrow x = 15
\]

But it asks for an inequality.

Perhaps:
> She paid $180 for tickets at $12 each. How many tickets did she buy?

Then:
\[
12x = 180 \Rightarrow x = 15
\]

But again, it says “inequality”.

Maybe the problem is:
> She paid at most $180 for tickets at $12 each.

Then:
\[
12x \leq 180 \Rightarrow x \leq 15
\]

Then maximum number = 15.

Let’s go with that.

a) Let \( x \) = number of tickets
\[
12x \leq 180
\]

b) Solve:
\[
x \leq 15
\]

So maximum number of tickets = 15

✔ Answer:
a) \( 12x \leq 180 \)
b) Maximum number = 15

---

Summary of Answers:

#### Problem 1:
- a) \( x = 50 - 30 \)
- b) \( x = 20 \) → Chris has $20 left.

(But note: Part b mentions "students", which seems misplaced.)

#### Problem 2:
- a) Let \( x \) = number who left
\( 630 - x \geq 400 \)
- b) \( x \leq 230 \) → Minimum number in club = 400

#### Problem 3:
- a) Let \( x \) = number of CDs
\( 4 + 12x < 85 \)
- b) \( x < 6.75 \) → Max number of CDs = 6

#### Problem 4:
- a) Let \( x \) = number of tickets
\( 12x \leq 180 \)
- b) \( x \leq 15 \) → Maximum number = 15

---

⚠️ Note: Several parts of the original problem seem misaligned or incomplete (e.g., "students in her class" in Problem 1). Please verify the exact wording if possible.

If you can provide the corrected full text or clarify any ambiguities, I can give even more accurate solutions!