Evaluating Algebraic Expression Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Evaluate the Expressions – Single Variable", which contains 10 algebraic expressions to evaluate for a given value of the variable (in this case, $ x = 11 $). Let's go through each problem step by step and evaluate them.

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Given:

$ x = 11 $

Now evaluate each expression:

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1. $ 3x + 6 $
Substitute $ x = 11 $:
$ 3(11) + 6 = 33 + 6 = \boxed{39} $

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2. $ 3x - 6 $
$ 3(11) - 6 = 33 - 6 = \boxed{27} $

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3. $ x^2 + 8 $
$ 11^2 + 8 = 121 + 8 = \boxed{129} $

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4. $ x + 5 $
$ 11 + 5 = \boxed{16} $

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5. $ \frac{x}{5} + 10 $
$ \frac{11}{5} + 10 = 2.2 + 10 = \boxed{12.2} $
*(or as a fraction: $ \frac{11}{5} + \frac{50}{5} = \frac{61}{5} $)*

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6. $ (-x) + 4 $
$ -11 + 4 = \boxed{-7} $

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7. $ x^2 - 8 $
$ 11^2 - 8 = 121 - 8 = \boxed{113} $

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8. $ \left(\frac{x}{2}\right)^2 + 3 $
First, $ \frac{11}{2} = 5.5 $, then square it:
$ (5.5)^2 = 30.25 $, then add 3:
$ 30.25 + 3 = \boxed{33.25} $
*(Or as a fraction: $ \left(\frac{11}{2}\right)^2 = \frac{121}{4} $, $ \frac{121}{4} + 3 = \frac{121}{4} + \frac{12}{4} = \frac{133}{4} $)*

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9. $ \frac{10}{x} + 8 $
$ \frac{10}{11} + 8 \approx 0.909 + 8 = \boxed{8.909} $
*(Exact: $ \frac{10}{11} + \frac{88}{11} = \frac{98}{11} $)*

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10. $ \frac{1}{x} + 4 $
$ \frac{1}{11} + 4 \approx 0.0909 + 4 = \boxed{4.0909} $
*(Exact: $ \frac{1}{11} + \frac{44}{11} = \frac{45}{11} $)*

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✔ Final Answers:

1. $ 39 $
2. $ 27 $
3. $ 129 $
4. $ 16 $
5. $ 12.2 $ or $ \frac{61}{5} $
6. $ -7 $
7. $ 113 $
8. $ 33.25 $ or $ \frac{133}{4} $
9. $ \frac{98}{11} $ or $ \approx 8.909 $
10. $ \frac{45}{11} $ or $ \approx 4.0909 $

Let me know if you'd like these answers formatted in a specific way (e.g., fractions only, decimals, etc.)!