Basic Algebra Worksheets - Free Printable

It looks like you've uploaded an image of a completed math worksheet titled "Calculate the Expression Sheet 3 Answers", which contains 25 algebraic expressions to evaluate given specific values for variables. The worksheet is already filled out with answers, so it appears to be an answer key.

However, since your request is to solve the problem and explain the solution, I'll go through how each expression is evaluated step by step using the provided variable values. This will help clarify the process behind each answer.

---

🔢 General Approach:

For each problem:
1. Substitute the given value of the variable into the expression.
2. Follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
3. Simplify to get the final result.

Let’s walk through a few examples in detail and then summarize the rest.

---

✔ Example 1:

Expression: $ 2a - 3 $, when $ a = 3 $

- Plug in: $ 2(3) - 3 $
- Multiply: $ 6 - 3 $
- Subtract: $ 3 $

But the answer shown is 7, which suggests a typo — unless $ a = 5 $? Let's check:

Wait! The answer says: 2×5 - 3 = 7

So likely, the original problem meant $ a = 5 $, not $ a = 3 $. But the "WHEN" column says $ a = 3 $. That’s a contradiction.

Let’s double-check:

> Problem 1: $ 2a - 3 $, $ a = 3 $ → should be $ 2×3 - 3 = 6 - 3 = 3 $

But the answer says 7, and shows $ 2×5 - 3 = 7 $. So either:
- There's a typo in the problem (should be $ a = 5 $), or
- The answer key has an error.

✔ Conclusion: Likely a typo. If $ a = 5 $, then $ 2×5 - 3 = 10 - 3 = 7 $ → correct.

So we assume $ a = 5 $ for problem 1.

---

✔ Example 2: $ 3b + 4 $, $ b = 5 $

- $ 3(5) + 4 = 15 + 4 = 19 $ ✔

✔️ Correct.

---

✔ Example 3: $ c - 10 $, $ c = 7 $

- $ 7 - 10 = -3 $ ✔

✔️ Correct.

---

✔ Example 4: $ 5d - 3 $, $ d = 20 $

- $ 5×20 = 100 $
- $ 100 - 3 = 97 $ ✔

✔️ Correct.

---

✔ Example 5: $ 3(e + 4) $, $ e = -1 $

- $ e + 4 = -1 + 4 = 3 $
- $ 3×3 = 9 $ ✔

✔️ Correct.

---

✔ Example 6: $ 7(f - 2) $, $ f = 10 $

- $ 10 - 2 = 8 $
- $ 7×8 = 56 $ ✔

✔️ Correct.

---

✔ Example 7: $ \frac{1}{2}(g + 2) $, $ g = 4 $

- $ g + 2 = 6 $
- $ \frac{1}{2} × 6 = 3 $ ✔

✔️ Correct.

---

✔ Example 8: $ (h - 2)/3 $, $ h = 11 $

- $ 11 - 2 = 9 $
- $ 9 ÷ 3 = 3 $ ✔

✔️ Correct.

---

✔ Example 9: $ i^2 $, $ i = 5 $

- $ 5^2 = 25 $ ✔

✔️ Correct.

---

✔ Example 10: $ j^2 - 5 $, $ j = 3 $

- $ 3^2 = 9 $
- $ 9 - 5 = 4 $ ✔

✔️ Correct.

---

✔ Example 11: $ 3(5 - k) $, $ k = 2 $

- $ 5 - 2 = 3 $
- $ 3×3 = 9 $ ✔

✔️ Correct.

---

✔ Example 12: $ \frac{1}{4}l - 7 $, $ l = 16 $

- $ \frac{1}{4} × 16 = 4 $
- $ 4 - 7 = -3 $ ✔

✔️ Correct.

---

✔ Example 13: $ (m - 4)/3 $, $ m = 10 $

- $ 10 - 4 = 6 $
- $ 6 ÷ 3 = 2 $ ✔

✔️ Correct.

---

✔ Example 14: $ 12/(n + 4) $, $ n = 2 $

- $ n + 4 = 6 $
- $ 12 ÷ 6 = 2 $ ✔

✔️ Correct.

---

✔ Example 15: $ o^3 $, $ o = 3 $

- $ 3^3 = 27 $ ✔

✔️ Correct.

---

✔ Example 16: $ (p - 1)^2 $, $ p = 8 $

- $ 8 - 1 = 7 $
- $ 7^2 = 49 $ ✔

✔️ Correct.

---

✔ Example 17: $ (q + 4)^2 $, $ q = 2 $

- $ 2 + 4 = 6 $
- $ 6^2 = 36 $ ✔

✔️ Correct.

---

✔ Example 18: $ 6(r + 5) $, $ r = -3 $

- $ -3 + 5 = 2 $
- $ 6×2 = 12 $ ✔

✔️ Correct.

---

✔ Example 19: $ \frac{s}{7} - 6 $, $ s = 21 $

- $ 21 ÷ 7 = 3 $
- $ 3 - 6 = -3 $ ✔

✔️ Correct.

---

✔ Example 20: $ t/(7 - 6) $, $ t = 5 $

- $ 7 - 6 = 1 $
- $ 5 ÷ 1 = 5 $ ✔

✔️ Correct.

---

✔ Example 21: $ u(4 + 3) $, $ u = 2 $

- $ 4 + 3 = 7 $
- $ 2×7 = 14 $ ✔

✔️ Correct.

---

✔ Example 22: $ (v - 5) ÷ 6 $, $ v = 23 $

- $ 23 - 5 = 18 $
- $ 18 ÷ 6 = 3 $ ✔

✔️ Correct.

---

✔ Example 23: $ (2w - 3) ÷ 4 $, $ w = 2 $

- $ 2×2 = 4 $
- $ 4 - 3 = 1 $
- $ 1 ÷ 4 = \frac{1}{4} $ ✔

✔️ Correct.

---

✔ Example 24: $ (x + 2)^2 $, $ x = 10 $

- $ 10 + 2 = 12 $
- $ 12^2 = 144 $ ✔

✔️ Correct.

---

✔ Example 25: $ \sqrt{y} $, $ y = 36 $

- $ \sqrt{36} = 6 $ or $ -6 $ (since both $ 6^2 $ and $ (-6)^2 = 36 $)

But in real numbers, the principal square root is $ 6 $, but since the question asks for $ \sqrt{y} $, and doesn't specify positive only, it's acceptable to say 6 or -6.

⚠️ Note: Technically, $ \sqrt{} $ denotes the principal (non-negative) square root, so $ \sqrt{36} = 6 $. However, if solving $ x^2 = 36 $, then $ x = \pm6 $. So depending on context, both may be accepted.

Here, the answer key says 6 or -6, which is slightly imprecise, but commonly accepted in middle school contexts.

---

🚨 Summary of Key Observations:

| Problem | Issue? | Explanation |
|--------|--------|-----------|
| 1 | ✘ Error | Answer shows $ 2×5 - 3 = 7 $, but $ a = 3 $ is listed. Should be $ 2×3 - 3 = 3 $. Either $ a = 5 $ or answer is wrong. Likely typo. |
| 2–25 | ✔ All correct | All other calculations are accurate. |

---

✔ Final Answer Summary (with correction):

| # | Expression | Value | Answer |
|---|------------|-------|--------|
| 1 | $ 2a - 3 $, $ a = 3 $ | $ 2×3 - 3 = 3 $ | Should be 3 (not 7) |
| 2 | $ 3b + 4 $, $ b = 5 $ | $ 15 + 4 = 19 $ | ✔ 19 |
| 3 | $ c - 10 $, $ c = 7 $ | $ 7 - 10 = -3 $ | ✔ -3 |
| ... | ... | ... | ... |
| 25 | $ \sqrt{y} $, $ y = 36 $ | $ \sqrt{36} = 6 $ | ✔ 6 (or ±6, depending on context) |

---

✔ Conclusion:

The worksheet is mostly correct, except for problem #1, which appears to have a mismatch between the variable value and the calculation. It likely should be:

> Problem 1: $ 2a - 3 $, when $ a = 5 $ → $ 2×5 - 3 = 10 - 3 = 7 $

Otherwise, all other answers are correct.

If this was a student's homework, they should double-check problem 1 for accuracy.

Let me know if you'd like a corrected version of the worksheet!