Evaluating Algebraic Expressions Worksheets - Math Monks - Free Printable

Problem: Evaluating Algebraic Expressions

We are tasked with evaluating several algebraic expressions for given values of variables. Let's solve each part step by step.

---

Part A: Evaluate the following expressions for \( x = 2 \)

#### 1) \( 2x \)
Substitute \( x = 2 \):
\[
2x = 2(2) = 4
\]

#### 2) \( \frac{x}{16} \)
Substitute \( x = 2 \):
\[
\frac{x}{16} = \frac{2}{16} = \frac{1}{8}
\]

#### 3) \( 18 - x \)
Substitute \( x = 2 \):
\[
18 - x = 18 - 2 = 16
\]

#### 4) \( \frac{36}{x} \)
Substitute \( x = 2 \):
\[
\frac{36}{x} = \frac{36}{2} = 18
\]

#### 5) \( 5x - 2 \)
Substitute \( x = 2 \):
\[
5x - 2 = 5(2) - 2 = 10 - 2 = 8
\]

#### 6) \( x + 28 \)
Substitute \( x = 2 \):
\[
x + 28 = 2 + 28 = 30
\]

#### 7) \( 2x - 3 \)
Substitute \( x = 2 \):
\[
2x - 3 = 2(2) - 3 = 4 - 3 = 1
\]

#### 8) \( 2 - 2x \)
Substitute \( x = 2 \):
\[
2 - 2x = 2 - 2(2) = 2 - 4 = -2
\]

---

Part B: Evaluate the following expressions for \( x = 3 \), \( y = 5 \)

#### 1) \( x - 2x + y \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
x - 2x + y = 3 - 2(3) + 5 = 3 - 6 + 5 = 2
\]

#### 2) \( 22 + 2x + 2y \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
22 + 2x + 2y = 22 + 2(3) + 2(5) = 22 + 6 + 10 = 38
\]

#### 3) \( 12x - y \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
12x - y = 12(3) - 5 = 36 - 5 = 31
\]

#### 4) \( -3 - x - y \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
-3 - x - y = -3 - 3 - 5 = -11
\]

#### 5) \( -4 - 2x - y \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
-4 - 2x - y = -4 - 2(3) - 5 = -4 - 6 - 5 = -15
\]

#### 6) \( 9x - y + 1 \)
Substitute \( x = 3 \) and \( y = 5 \):
\[
9x - y + 1 = 9(3) - 5 + 1 = 27 - 5 + 1 = 23
\]

---

Part C: Evaluate the following expressions for \( a = 1 \), \( b = 4 \)

#### 7) \( \frac{6a}{b} \)
Substitute \( a = 1 \) and \( b = 4 \):
\[
\frac{6a}{b} = \frac{6(1)}{4} = \frac{6}{4} = \frac{3}{2}
\]

#### 8) \( \frac{4}{a} + b \)
Substitute \( a = 1 \) and \( b = 4 \):
\[
\frac{4}{a} + b = \frac{4}{1} + 4 = 4 + 4 = 8
\]

#### 9) \( \frac{a}{b} + 1 \)
Substitute \( a = 1 \) and \( b = 4 \):
\[
\frac{a}{b} + 1 = \frac{1}{4} + 1 = \frac{1}{4} + \frac{4}{4} = \frac{5}{4}
\]

---

Final Answers:

Part A:
1) \( 4 \)
2) \( \frac{1}{8} \)
3) \( 16 \)
4) \( 18 \)
5) \( 8 \)
6) \( 30 \)
7) \( 1 \)
8) \( -2 \)

Part B:
1) \( 2 \)
2) \( 38 \)
3) \( 31 \)
4) \( -11 \)
5) \( -15 \)
6) \( 23 \)

Part C:
7) \( \frac{3}{2} \)
8) \( 8 \)
9) \( \frac{5}{4} \)

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Part A:} & 4, \frac{1}{8}, 16, 18, 8, 30, 1, -2 \\
\text{Part B:} & 2, 38, 31, -11, -15, 23 \\
\text{Part C:} & \frac{3}{2}, 8, \frac{5}{4}
\end{array}
}
\]