Evaluating Algebraic Expression Worksheets - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Evaluate the Expressions: Multi-variables", with several algebraic expressions to evaluate for given values of variables.

Since I can't view images directly, I'll need you to provide the text or describe the problems from the image. However, based on your description and the visible content in your message (which seems to be a transcription), here is what I see:

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Problem Set:

Evaluate the algebraic expressions for the given values of each variable.

1. $ 2x + 3y $ when $ x = -4, y = -5 $
2. $ \frac{3}{4}p + 3r + 2q $ when $ p = 2, q = -4, r = 6 $
3. $ 6a^2 + 6b $ when $ a = -2, b = -1 $
4. $ 9s + 4q + t $ when $ s = 2, q = -8, t = 5 $
5. $ 7pp + 2m $ when $ p = -3, m = 2 $
6. $ 6a^2 $ when $ a = -2 $
7. $ 6b + 2c $ when $ b = 2, c = -4 $
8. $ \frac{2}{3}x - 3 $ when $ x = -9 $

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Let me solve each one step by step.

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1. $ 2x + 3y $, where $ x = -4, y = -5 $

$$
2(-4) + 3(-5) = -8 - 15 = -23
$$

✔ Answer: $ -23 $

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2. $ \frac{3}{4}p + 3r + 2q $, where $ p = 2, q = -4, r = 6 $

$$
\frac{3}{4}(2) + 3(6) + 2(-4) = \frac{6}{4} + 18 - 8 = 1.5 + 10 = 11.5
$$

Or as a fraction:
$ \frac{3}{2} + 10 = \frac{3}{2} + \frac{20}{2} = \frac{23}{2} $

✔ Answer: $ \frac{23}{2} $ or $ 11.5 $

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3. $ 6a^2 + 6b $, where $ a = -2, b = -1 $

Note: $ a^2 = (-2)^2 = 4 $

$$
6(4) + 6(-1) = 24 - 6 = 18
$$

✔ Answer: $ 18 $

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4. $ 9s + 4q + t $, where $ s = 2, q = -8, t = 5 $

$$
9(2) + 4(-8) + 5 = 18 - 32 + 5 = -9
$$

✔ Answer: $ -9 $

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5. $ 7pp + 2m $, where $ p = -3, m = 2 $

Note: $ pp = p^2 = (-3)^2 = 9 $

$$
7(9) + 2(2) = 63 + 4 = 67
$$

✔ Answer: $ 67 $

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6. $ 6a^2 $, where $ a = -2 $

$$
6(-2)^2 = 6(4) = 24
$$

✔ Answer: $ 24 $

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7. $ 6b + 2c $, where $ b = 2, c = -4 $

$$
6(2) + 2(-4) = 12 - 8 = 4
$$

✔ Answer: $ 4 $

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8. $ \frac{2}{3}x - 3 $, where $ x = -9 $

$$
\frac{2}{3}(-9) - 3 = -6 - 3 = -9
$$

✔ Answer: $ -9 $

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✔ Final Answers:

1. $ -23 $
2. $ \frac{23}{2} $ or $ 11.5 $
3. $ 18 $
4. $ -9 $
5. $ 67 $
6. $ 24 $
7. $ 4 $
8. $ -9 $

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