Simplifying Algebraic Expressions worksheet with ten problems requiring substitution and simplification.

Let's solve each problem step by step, simplifying the algebraic expressions and substituting the given values.

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1) $ h + 3h $ use $ h = 4 $

Combine like terms:
$ h + 3h = 4h $

Now substitute $ h = 4 $:
$ 4(4) = 16 $

✔ Answer: 16

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2) $ \frac{h}{4} + 2 $ use $ h = -12 $

Substitute $ h = -12 $:
$ \frac{-12}{4} + 2 = -3 + 2 = -1 $

✔ Answer: -1

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3) $ -5(2x + 6) $ use $ x = -3 $

First distribute:
$ -5(2x + 6) = -10x - 30 $

Now substitute $ x = -3 $:
$ -10(-3) - 30 = 30 - 30 = 0 $

✔ Answer: 0

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4) $ -9h + 6(8 + 4h) $ use $ h = -6 $

Distribute first:
$ -9h + 6(8 + 4h) = -9h + 48 + 24h $

Combine like terms:
$ (-9h + 24h) + 48 = 15h + 48 $

Now substitute $ h = -6 $:
$ 15(-6) + 48 = -90 + 48 = -42 $

✔ Answer: -42

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5) $ 7 - \frac{f}{4} + 6f $ use $ f = 16 $

Substitute $ f = 16 $:
$ 7 - \frac{16}{4} + 6(16) = 7 - 4 + 96 = 3 + 96 = 99 $

✔ Answer: 99

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6) $ -7(-3 - 2r) $ use $ r = -3 $

First simplify inside parentheses:
$ -3 - 2(-3) = -3 + 6 = 3 $

Now multiply:
$ -7(3) = -21 $

Alternatively, distribute first:
$ -7(-3 - 2r) = 21 + 14r $

Now substitute $ r = -3 $:
$ 21 + 14(-3) = 21 - 42 = -21 $

✔ Answer: -21

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7) $ 2 - \frac{r}{3} $ use $ r = -6 $

Substitute $ r = -6 $:
$ 2 - \frac{-6}{3} = 2 - (-2) = 2 + 2 = 4 $

✔ Answer: 4

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8) $ -4(-9 - 5x) + 6 $ use $ x = 9 $

First distribute:
$ -4(-9 - 5x) = 36 + 20x $

Then add 6:
$ 36 + 20x + 6 = 42 + 20x $

Now substitute $ x = 9 $:
$ 42 + 20(9) = 42 + 180 = 222 $

✔ Answer: 222

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9) $ 6x + 3x - 9 $ use $ x = 6 $

Combine like terms:
$ (6x + 3x) - 9 = 9x - 9 $

Substitute $ x = 6 $:
$ 9(6) - 9 = 54 - 9 = 45 $

✔ Answer: 45

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10) $ 4f - f $ use $ f = 9 $

Simplify:
$ 4f - f = 3f $

Substitute $ f = 9 $:
$ 3(9) = 27 $

✔ Answer: 27

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✔ Final Answers:

1) 16
2) -1
3) 0
4) -42
5) 99
6) -21
7) 4
8) 222
9) 45
10) 27

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