One-Step Inequality Word Problems | Interactive Worksheet ... - Free Printable

Here’s the solution to each one-step inequality word problem, with explanations:

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Problem 1:

> Lara wants to make room on her bookshelf for some new books. After she donates 14 books to her local library, she still has 50 books left on her bookshelf. How many books did Lara originally have on her bookshelf?

✔ Inequality Setup:
Let *x* = number of books Lara originally had.

She donates 14 books → remaining books = x – 14
We’re told she has at least 50 books left (since she “still has 50 books left” — implying that’s what remains after removing 14).

So:
> x – 14 ≥ 50

✔ Solve:
Add 14 to both sides:
> x ≥ 64

✔ Fill in the blank:
> Lara had more than 64 books on her bookshelf.

*(Note: Since she donated 14 and had 50 left, she must have had at least 64. The phrase “more than” is slightly imprecise here — technically it should be “at least 64”, but since the blank says “more than”, and 64 is the minimum, we can say “more than 64” if we interpret it as “not less than 64”. But strictly speaking, 64 is included. However, in many elementary contexts, “more than” is used loosely. To match the phrasing, we’ll write 64.)*

Actually — let’s check the wording: “How many books did Lara originally have?” — it’s a definite number, not an inequality. But the instruction says to write an inequality.

Wait — rereading: “Write and solve an inequality... then fill in the blank.”

The key is: She still has 50 books left — meaning after donating 14, she has exactly 50? Or at least 50?

The problem says “she still has 50 books left” — this implies exactly 50. But then why ask for an inequality?

Ah — perhaps the intent is that she wants to make room, so she needs to reduce her collection. She donates 14 and ends up with 50 — so originally she had 64. But the problem asks for an inequality.

Actually — maybe the problem is misphrased. Let’s assume the intent is:

She wants to have no more than 50 books after donating 14. So original books minus 14 ≤ 50 → x ≤ 64? That doesn’t make sense.

Alternatively — perhaps she has at least 50 left after donating 14, meaning she originally had at least 64.

Given the context of “make room”, she likely had more than 50, and after donating 14, she has 50 — so original = 64.

But since the problem says “write an inequality”, and “fill in the blank” with “more than ___”, we’ll go with:

> x – 14 ≥ 50 → x ≥ 64

So:

> Lara had more than 64 books on her bookshelf.

*(Technically, she had at least 64 — including 64. But “more than 64” would exclude 64. This is a common issue in word problems. In most classroom settings, they accept 64 as the answer even if it says “more than”. Alternatively, perhaps the problem meant she has “at least 50 left”, so original ≥ 64. We’ll proceed with 64.)*

✔ Final Answer for #1: 64

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Problem 2:

> Colin has 45 minutes until he needs to leave for his piano lesson. He spends 27 minutes watching an episode of his favorite TV show. Then he wants to play a game on his laptop. At most, how long can Colin spend playing the game before he needs to leave?

✔ Inequality Setup:
Let *t* = time (in minutes) Colin can spend playing the game.

Time spent watching TV + time playing game ≤ total time available

> 27 + t ≤ 45

✔ Solve:
Subtract 27 from both sides:
> t ≤ 18

✔ Fill in the blank:
> Colin can play the game for at most 18 minutes.

✔ Final Answer for #2: 18

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Problem 3:

> The owner of Charlotte’s Chocolates moves a display of boxes of truffles to the front of the store. Each box costs $20. The owner hopes to sell at least $120 worth of truffles this month. What is the minimum number of boxes she needs to sell this month?

✔ Inequality Setup:
Let *b* = number of boxes sold.

Each box = $20 → total revenue = 20b

She wants at least $120:

> 20b ≥ 120

✔ Solve:
Divide both sides by 20:
> b ≥ 6

✔ Fill in the blank:
> The owner needs to sell at least 6 boxes of truffles.

✔ Final Answer for #3: 6

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Problem 4:

> Eleanor has a budget for each day. On Tuesday morning, she spends $3.25 on a smoothie from Healthy Smoothie Hut. She needs to spend less than $12.75 to stay within her budget. How much more can she spend on Tuesday?

✔ Inequality Setup:
Let *s* = additional amount she can spend on Tuesday.

She already spent $3.25 → total spending = 3.25 + s

She must spend less than $12.75:

> 3.25 + s < 12.75

✔ Solve:
Subtract 3.25 from both sides:
> s < 9.50

✔ Fill in the blank:
> Eleanor wants to spend less than $9.50 on Tuesday.

✔ Final Answer for #4: $9.50

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## ✔ Final Answers:

1. 64
2. 18
3. 6
4. $9.50

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## 📝 Explanation Summary:

- For each problem, we identified the unknown quantity and wrote an inequality based on the condition (“at least”, “at most”, “less than”, etc.).
- We solved the inequality using inverse operations (addition/subtraction or multiplication/division).
- We interpreted the result in the context of the problem and filled in the blank accordingly.

These are classic one-step inequalities — great practice for understanding real-world applications of algebra!