Evaluating Expressions with Variables Worksheet (printable, online ... - Free Printable

Let’s solve each expression one by one. We’ll plug in the given values for the variables and simplify step by step.

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1. Evaluate:
\(\frac{w}{6} - 4k\), if \(w = 18\), \(k = -4\)

Step 1: Plug in the values.
→ \(\frac{18}{6} - 4(-4)\)

Step 2: Simplify division and multiplication.
→ \(3 - (-16)\) → because \(4 × -4 = -16\), but there’s a minus sign before it, so it becomes +16

Step 3: Add.
→ \(3 + 16 = 19\)

✔ Answer: 19

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2. Evaluate:
\(9z - \frac{k}{8}\), if \(z = 5\), \(k = -24\)

Step 1: Plug in the values.
→ \(9(5) - \frac{-24}{8}\)

Step 2: Multiply and divide.
→ \(45 - (-3)\) → because \(-24 ÷ 8 = -3\)

Step 3: Subtracting a negative is adding.
→ \(45 + 3 = 48\)

✔ Answer: 48

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3. Evaluate:
\(c - 5x\), if \(c = 4\), \(x = -9\)

Step 1: Plug in the values.
→ \(4 - 5(-9)\)

Step 2: Multiply first.
→ \(4 - (-45)\) → because \(5 × -9 = -45\)

Step 3: Subtracting a negative is adding.
→ \(4 + 45 = 49\)

✔ Answer: 49

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4. Evaluate:
\(9s + 7x\), if \(x = -4\), \(s = -8\)

Step 1: Plug in the values.
→ \(9(-8) + 7(-4)\)

Step 2: Multiply both terms.
→ \(-72 + (-28)\)

Step 3: Add (both are negative).
→ \(-72 - 28 = -100\)

✔ Answer: -100

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5. Evaluate:
\(11 + 5x - 6r\), if \(x = -9\), \(r = -3\)

Step 1: Plug in the values.
→ \(11 + 5(-9) - 6(-3)\)

Step 2: Multiply.
→ \(11 + (-45) - (-18)\)

Step 3: Simplify signs.
→ \(11 - 45 + 18\)

Step 4: Work left to right.
→ \(11 - 45 = -34\)
→ \(-34 + 18 = -16\)

✔ Answer: -16

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6. Evaluate:
\(5 + \frac{f}{-5} + 6z\), if \(f = -15\), \(z = -7\)

Step 1: Plug in the values.
→ \(5 + \frac{-15}{-5} + 6(-7)\)

Step 2: Divide and multiply.
→ \(5 + 3 + (-42)\) → because \(-15 ÷ -5 = 3\), and \(6 × -7 = -42\)

Step 3: Add from left to right.
→ \(5 + 3 = 8\)
→ \(8 + (-42) = -34\)

✔ Answer: -34

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7. Evaluate:
\(11 + 5x - 6r\), if \(x = -9\), \(f = -3\) ← Wait! The variable here is “f”, but the expression uses “r”. That must be a typo. Looking back at problem #5, it was “r” with value -3. Probably meant to say “r = -3” again? But here it says “f = -3”. Let’s check the original image — actually, looking closely, this might be a copy-paste error in the worksheet. Since the expression has “r”, and no value for r is given, but f is given… that doesn’t make sense.

Wait — let me re-read:
“11+5x−6r, if x=−9,f=−3”

This seems like a mistake. The expression uses “r”, but they give you “f”. Maybe it’s supposed to be “r = -3”? Because in problem #5, same expression had r = -3. Or maybe it’s a different variable? But “f” isn’t in the expression.

Actually — looking at the last problem, it uses “d”, so maybe this is a typo and should be “r = -3”? I think we have to assume that “f = -3” is a typo and it should be “r = -3”, since otherwise the problem can’t be solved.

Alternatively — perhaps the expression was meant to be “11 + 5x - 6f”? Then we could use f = -3.

But the expression clearly says “-6r”.

Given that in problem #5, same expression used r = -3, and here they wrote “f = -3”, it’s likely a typo and they meant r = -3.

So I’ll proceed assuming r = -3.

→ So: \(11 + 5(-9) - 6(-3)\)

Same as problem #5!

→ \(11 - 45 + 18 = -16\)

✔ Answer: -16 *(assuming r = -3)*

If it really is f = -3 and expression has r, then it’s unsolvable — but that’s unlikely. So we go with -16.

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8. Evaluate:
\(-9c - 3 + 5d\), if \(c = 7\), \(d = -6\)

Step 1: Plug in the values.
→ \(-9(7) - 3 + 5(-6)\)

Step 2: Multiply.
→ \(-63 - 3 + (-30)\)

Step 3: Add/subtract left to right.
→ \(-63 - 3 = -66\)
→ \(-66 + (-30) = -96\)

✔ Answer: -96

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Final Answers:

1. 19
2. 48
3. 49
4. -100
5. -16
6. -34
7. -16 *(assuming r = -3 due to typo)*
8. -96

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Final Answer:
19, 48, 49, -100, -16, -34, -16, -96