Pre-Algebra Worksheets | Algebraic Expressions Worksheets - Free Printable

Problem: Simplifying Algebraic Expressions

We are tasked with simplifying each algebraic expression by substituting the given values for the variables and performing the necessary calculations. Let's solve each problem step by step.

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#### 1) \( 9 + 4f - 7z \)
- Given: \( f = 6 \) and \( z = 5 \)
- Substitute the values:
\[
9 + 4(6) - 7(5)
\]
- Perform the multiplications:
\[
9 + 24 - 35
\]
- Perform the addition and subtraction:
\[
9 + 24 = 33
\]
\[
33 - 35 = -2
\]
- Answer: \(\boxed{-2}\)

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#### 2) \( 8(9d + 6) - 4b \)
- Given: \( d = 8 \) and \( b = 3 \)
- Substitute the values:
\[
8(9(8) + 6) - 4(3)
\]
- Perform the multiplication inside the parentheses:
\[
9(8) = 72
\]
\[
72 + 6 = 78
\]
- Now, multiply by 8:
\[
8(78) = 624
\]
- Subtract \( 4b \):
\[
624 - 4(3) = 624 - 12 = 612
\]
- Answer: \(\boxed{612}\)

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#### 3) \( -3w + 2(8x - 9) \)
- Given: \( x = 5 \) and \( w = 7 \)
- Substitute the values:
\[
-3(7) + 2(8(5) - 9)
\]
- Perform the multiplication inside the parentheses:
\[
8(5) = 40
\]
\[
40 - 9 = 31
\]
- Multiply by 2:
\[
2(31) = 62
\]
- Perform the remaining multiplication:
\[
-3(7) = -21
\]
- Add the results:
\[
-21 + 62 = 41
\]
- Answer: \(\boxed{41}\)

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#### 4) \( -\frac{k}{8} \cdot 8h \)
- Given: \( k = 24 \) and \( h = 7 \)
- Substitute the values:
\[
-\frac{24}{8} \cdot 8(7)
\]
- Simplify the fraction:
\[
\frac{24}{8} = 3
\]
\[
-\frac{24}{8} = -3
\]
- Multiply by \( 8h \):
\[
-3 \cdot 8(7) = -3 \cdot 56 = -168
\]
- Answer: \(\boxed{-168}\)

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#### 5) \( 7b + 4z \)
- Given: \( b = 6 \) and \( z = 7 \)
- Substitute the values:
\[
7(6) + 4(7)
\]
- Perform the multiplications:
\[
7(6) = 42
\]
\[
4(7) = 28
\]
- Add the results:
\[
42 + 28 = 70
\]
- Answer: \(\boxed{70}\)

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#### 6) \( -9n + 5 - 3x - 6 \)
- Given: \( n = 9 \) and \( x = 2 \)
- Substitute the values:
\[
-9(9) + 5 - 3(2) - 6
\]
- Perform the multiplications:
\[
-9(9) = -81
\]
\[
-3(2) = -6
\]
- Combine all terms:
\[
-81 + 5 - 6 - 6
\]
- Perform the additions and subtractions:
\[
-81 + 5 = -76
\]
\[
-76 - 6 = -82
\]
\[
-82 - 6 = -88
\]
- Answer: \(\boxed{-88}\)

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#### 7) \( \frac{21}{x} - 2s \)
- Given: \( x = 7 \) and \( s = 9 \)
- Substitute the values:
\[
\frac{21}{7} - 2(9)
\]
- Simplify the division:
\[
\frac{21}{7} = 3
\]
- Perform the multiplication:
\[
2(9) = 18
\]
- Subtract the results:
\[
3 - 18 = -15
\]
- Answer: \(\boxed{-15}\)

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#### 8) \( -3(-6n - 4s) \)
- Given: \( s = 7 \) and \( n = 9 \)
- Substitute the values:
\[
-3(-6(9) - 4(7))
\]
- Perform the multiplications inside the parentheses:
\[
-6(9) = -54
\]
\[
-4(7) = -28
\]
- Add the results inside the parentheses:
\[
-54 - 28 = -82
\]
- Multiply by \(-3\):
\[
-3(-82) = 246
\]
- Answer: \(\boxed{246}\)

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#### 9) \( 7(4r + 6k) \)
- Given: \( r = 9 \) and \( k = 2 \)
- Substitute the values:
\[
7(4(9) + 6(2))
\]
- Perform the multiplications inside the parentheses:
\[
4(9) = 36
\]
\[
6(2) = 12
\]
- Add the results inside the parentheses:
\[
36 + 12 = 48
\]
- Multiply by 7:
\[
7(48) = 336
\]
- Answer: \(\boxed{336}\)

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#### 10) \( 5k + 4x + 8 + 9 \)
- Given: \( k = 9 \) and \( x = 3 \)
- Substitute the values:
\[
5(9) + 4(3) + 8 + 9
\]
- Perform the multiplications:
\[
5(9) = 45
\]
\[
4(3) = 12
\]
- Add all the terms:
\[
45 + 12 + 8 + 9 = 74
\]
- Answer: \(\boxed{74}\)

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Final Answers:

\[
\boxed{-2, 612, 41, -168, 70, -88, -15, 246, 336, 74}
\]