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.