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The worksheet you uploaded is focused on evaluating algebraic expressions for given values of variables. I will guide you through solving the problems step by step.

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

1. \(\frac{10x}{2}\)
   - Substitute \(x = 2\):
   \[
   \frac{10 \times 2}{2} = \frac{20}{2} = 10
   \]

2. \(\frac{7x}{16}\)
   - Substitute \(x = 2\):
   \[
   \frac{7 \times 2}{16} = \frac{14}{16} = \frac{7}{8}
   \]

3. \(\frac{18 - x}{4}\)
   - Substitute \(x = 2\):
   \[
   \frac{18 - 2}{4} = \frac{16}{4} = 4
   \]

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

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

6. \(6x + 28\)
   - Substitute \(x = 2\):
   \[
   6 \times 2 + 28 = 12 + 28 = 40
   \]

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

8. \(9x^2 - 2x + 3\)
   - Substitute \(x = 2\):
   \[
   9 \times 2^2 - 2 \times 2 + 3 = 9 \times 4 - 4 + 3 = 36 - 4 + 3 = 35
   \]

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

1. \( x + 2x + y \)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   3 + 2 \times 3 + 5 = 3 + 6 + 5 = 14
   \]

2. \(2x^2 + 2xy\)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   2 \times 3^2 + 2 \times 3 \times 5 = 2 \times 9 + 30 = 18 + 30 = 48
   \]

3. \(x^2 - y\)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   3^2 - 5 = 9 - 5 = 4
   \]

4. \(3x - 3y\)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   3 \times 3 - 3 \times 5 = 9 - 15 = -6
   \]

5. \(9 - 4x - y\)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   9 - 4 \times 3 - 5 = 9 - 12 - 5 = -8
   \]

6. \(9x + y + 1\)
   - Substitute \(x = 3\) and \(y = 5\):
   \[
   9 \times 3 + 5 + 1 = 27 + 5 + 1 = 33
   \]

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

1. \(\frac{6a}{b}\)
   - Substitute \(a = 1\) and \(b = 4\):
   \[
   \frac{6 \times 1}{4} = \frac{6}{4} = \frac{3}{2}
   \]

2. \(\frac{ab}{a + b}\)
   - Substitute \(a = 1\) and \(b = 4\):
   \[
   \frac{1 \times 4}{1 + 4} = \frac{4}{5}
   \]

3. \(a^2 + b - 1\)
   - Substitute \(a = 1\) and \(b = 4\):
   \[
   1^2 + 4 - 1 = 1 + 4 - 1 = 4
   \]

Would you like to go over any specific part in more detail or have any questions?

Here are 5 additional related questions you can try:

1. How would you evaluate the expression \(4x + 3y - 2z\) if \(x = 1\), \(y = 2\), and \(z = 3\)?
2. Can you simplify and evaluate the expression \(2(a + b) + 3b\) when \(a = 3\) and \(b = 5\)?
3. What happens if you substitute negative values for \(x\) and \(y\) in the expression \(x^2 - y\)?
4. How do you approach evaluating an expression that contains multiple variables and exponents, like \(2x^3 + 3y^2 - z\)?
5. If you need to evaluate an expression like \( \frac{3x + 4y}{x - y}\), what happens when \(x = y\)?

**Tip:** Always double-check your substitutions to avoid simple mistakes when working with algebraic expressions.

Evaluate the following algebraic expressions for given values of variables.

Learn how to evaluate algebraic expressions for specific values of variables with a detailed step-by-step solution. This worksheet includes various expressions involving basic arithmetic operations and is suitable for students in Grades 6-8.

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