Basic Algebra Worksheets - Free Printable

Problem Description:

The task is to calculate the value of each given algebraic expression when the variable is substituted with a specific value. The expressions and their corresponding values are listed in the table. Below, I will verify each calculation step by step.

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Solution:

#### 1) \( 2a - 3 \) when \( a = 3 \)
\[
2a - 3 = 2(3) - 3 = 6 - 3 = 3
\]
Answer: \( 3 \)

#### 2) \( 3b + 4 \) when \( b = 5 \)
\[
3b + 4 = 3(5) + 4 = 15 + 4 = 19
\]
Answer: \( 19 \)

#### 3) \( c - 10 \) when \( c = 7 \)
\[
c - 10 = 7 - 10 = -3
\]
Answer: \( -3 \)

#### 4) \( 5d - 3 \) when \( d = 20 \)
\[
5d - 3 = 5(20) - 3 = 100 - 3 = 97
\]
Answer: \( 97 \)

#### 5) \( 3(e + 4) \) when \( e = -1 \)
\[
3(e + 4) = 3(-1 + 4) = 3(3) = 9
\]
Answer: \( 9 \)

#### 6) \( 7(f - 2) \) when \( f = 10 \)
\[
7(f - 2) = 7(10 - 2) = 7(8) = 56
\]
Answer: \( 56 \)

#### 7) \( \frac{1}{2}(g + 2) \) when \( g = 4 \)
\[
\frac{1}{2}(g + 2) = \frac{1}{2}(4 + 2) = \frac{1}{2}(6) = 3
\]
Answer: \( 3 \)

#### 8) \( \frac{(h - 2)}{3} \) when \( h = 11 \)
\[
\frac{(h - 2)}{3} = \frac{(11 - 2)}{3} = \frac{9}{3} = 3
\]
Answer: \( 3 \)

#### 9) \( i^2 \) when \( i = 5 \)
\[
i^2 = 5^2 = 25
\]
Answer: \( 25 \)

#### 10) \( j^2 - 5 \) when \( j = 3 \)
\[
j^2 - 5 = 3^2 - 5 = 9 - 5 = 4
\]
Answer: \( 4 \)

#### 11) \( 3(5 - k) \) when \( k = 2 \)
\[
3(5 - k) = 3(5 - 2) = 3(3) = 9
\]
Answer: \( 9 \)

#### 12) \( \frac{l}{4} - 7 \) when \( l = 16 \)
\[
\frac{l}{4} - 7 = \frac{16}{4} - 7 = 4 - 7 = -3
\]
Answer: \( -3 \)

#### 13) \( \frac{(m - 4)}{3} \) when \( m = 10 \)
\[
\frac{(m - 4)}{3} = \frac{(10 - 4)}{3} = \frac{6}{3} = 2
\]
Answer: \( 2 \)

#### 14) \( \frac{12}{(n + 4)} \) when \( n = 2 \)
\[
\frac{12}{(n + 4)} = \frac{12}{(2 + 4)} = \frac{12}{6} = 2
\]
Answer: \( 2 \)

#### 15) \( o^3 \) when \( o = 3 \)
\[
o^3 = 3^3 = 27
\]
Answer: \( 27 \)

#### 16) \( (p - 1)^2 \) when \( p = 8 \)
\[
(p - 1)^2 = (8 - 1)^2 = 7^2 = 49
\]
Answer: \( 49 \)

#### 17) \( (q + 4)^2 \) when \( q = 2 \)
\[
(q + 4)^2 = (2 + 4)^2 = 6^2 = 36
\]
Answer: \( 36 \)

#### 18) \( 6(r + 5) \) when \( r = -3 \)
\[
6(r + 5) = 6(-3 + 5) = 6(2) = 12
\]
Answer: \( 12 \)

#### 19) \( \frac{s}{7} - 6 \) when \( s = 21 \)
\[
\frac{s}{7} - 6 = \frac{21}{7} - 6 = 3 - 6 = -3
\]
Answer: \( -3 \)

#### 20) \( t / (7 - 6) \) when \( t = 5 \)
\[
t / (7 - 6) = 5 / (7 - 6) = 5 / 1 = 5
\]
Answer: \( 5 \)

#### 21) \( u(4 + 3) \) when \( u = 2 \)
\[
u(4 + 3) = 2(4 + 3) = 2(7) = 14
\]
Answer: \( 14 \)

#### 22) \( (v - 5) / 6 \) when \( v = 23 \)
\[
(v - 5) / 6 = (23 - 5) / 6 = 18 / 6 = 3
\]
Answer: \( 3 \)

#### 23) \( (2w - 3) / 4 \) when \( w = 2 \)
\[
(2w - 3) / 4 = (2(2) - 3) / 4 = (4 - 3) / 4 = 1 / 4 = \frac{1}{4}
\]
Answer: \( \frac{1}{4} \)

#### 24) \( (x + 2)^2 \) when \( x = 10 \)
\[
(x + 2)^2 = (10 + 2)^2 = 12^2 = 144
\]
Answer: \( 144 \)

#### 25) \( \sqrt{y} \) when \( y = 36 \)
\[
\sqrt{y} = \sqrt{36} = 6 \text{ or } -6
\]
Answer: \( 6 \text{ or } -6 \)

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Final Answer:

\[
\boxed{3, 19, -3, 97, 9, 56, 3, 3, 25, 4, 9, -3, 2, 2, 27, 49, 36, 12, -3, 5, 14, 3, \frac{1}{4}, 144, 6 \text{ or } -6}
\]