Math worksheet for evaluating algebraic expressions with variables.

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

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1. q - r - (-1) when q = 1, r = 7

Plug in:
1 - 7 - (-1)
= 1 - 7 + 1 (because minus a negative is plus)
= (1 + 1) - 7
= 2 - 7
= -5

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2. (7x + 5)/(-5) when x = -3

Plug in:
(7*(-3) + 5)/(-5)
= (-21 + 5)/(-5)
= (-16)/(-5)
= 16/5 or 3.2

But since it’s algebra, we can leave as fraction: 16/5

Wait — let me double-check:

7 * -3 = -21
-21 + 5 = -16
-16 divided by -5 = positive 16/5 → yes.

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3. q³ - 3q + 12 at q = -5

Plug in:
(-5)³ - 3*(-5) + 12
= -125 + 15 + 12
= (-125) + 27
= -98

Check:
(-5)^3 = -125
-3 * -5 = +15
So: -125 + 15 = -110; -110 + 12 = -98 → correct.

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4. c/2 - 1 at c = 16

Plug in:
16/2 - 1 = 8 - 1 = 7

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5. (9v - 23)/5 at v = 7

Plug in:
(9*7 - 23)/5 = (63 - 23)/5 = 40/5 = 8

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6. (b² - 4b)² at b = -2

First, inside the parentheses:
b² = (-2)² = 4
4b = 4*(-2) = -8
So: 4 - (-8) = 4 + 8 = 12
Then square it: 12² = 144

Wait — expression is (b² - 4b)²

So: b² - 4b = 4 - (-8)? No!

Hold on: 4b means 4 times b → 4 * (-2) = -8

So: b² - 4b = 4 - (-8)? NO! It’s 4 minus (4b), which is 4 - (-8)? Wait no:

Actually: b² - 4b = [(-2)^2] - [4*(-2)] = 4 - (-8) = 4 + 8 = 12 → then squared = 144 → correct.

Yes.

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7. 6q(q + 7)² at q = -5

First, compute (q + 7) = -5 + 7 = 2
Then square it: 2² = 4
Now multiply: 6 * q * 4 = 6 * (-5) * 4
= -30 * 4 = -120

Check order: 6q(q+7)² → so 6 * (-5) * (2)^2 = 6*-5*4 = -120 → correct.

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8. 4/(12 - 2y) + 3 at y = 5

First, denominator: 12 - 2*5 = 12 - 10 = 2
So: 4/2 + 3 = 2 + 3 = 5

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9. (y + 1)^4 at y = -2

y + 1 = -2 + 1 = -1
(-1)^4 = 1 (since even power) → 1

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10. 5(k + 9) at k = -14

k + 9 = -14 + 9 = -5
5 * (-5) = -25

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Now let’s list all answers clearly:

1. -5
2. 16/5 (or 3.2, but fraction is better)
3. -98
4. 7
5. 8
6. 144
7. -120
8. 5
9. 1
10. -25

I’ll write them as numbers, and for #2, I’ll use fraction unless decimal is specified — but since others are integers, maybe keep as fraction.

Actually, looking back at problem 2: it says “evaluate”, and answer could be fractional. But let’s see if they expect simplified form.

In math worksheets, often fractions are preferred unless told otherwise.

But 16/5 is fine. Alternatively, mixed number? Probably not needed.

I think 16/5 is acceptable.

But let me check if I made any mistake.

Problem 2 again: (7x +5)/(-5), x=-3

7*(-3)= -21; -21+5= -16; -16 / -5 = 16/5 → yes.

Okay.

Final Answers:

1. -5
2. 16/5
3. -98
4. 7
5. 8
6. 144
7. -120
8. 5
9. 1
10. -25

I’ll box them as per instruction.

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Final Answer:
1. -5
2. \frac{16}{5}
3. -98
4. 7
5. 8
6. 144
7. -120
8. 5
9. 1
10. -25