Let's work on the questions from the image:

1) Simplifying Fractions:

The following fractions need to be simplified.

a) $\frac{25}{35}$

• You divided both numerator and denominator by 5, simplifying to: $\frac{25}{35} = \frac{5}{7}$

f) $\frac{4 \times 5}{35}$

• Multiply the numerator: $4 \times 5 = 20$, resulting in: $\frac{20}{35} = \frac{4}{7}$ (You mistakenly wrote 9/7. The correct answer is $\frac{4}{7}$).

2) Solving the equation:

$\frac{3x + 5}{4} - \frac{2x - 3}{3} = 3$ To solve this, let's follow these steps:

Step 1: Find a common denominator. The least common denominator (LCD) between 4 and 3 is 12.

• Multiply the first term by 3/3 and the second term by 4/4: $\frac{3(3x + 5)}{12} - \frac{4(2x - 3)}{12} = 3$ This simplifies to: $\frac{9x + 15}{12} - \frac{8x - 12}{12} = 3$

Step 2: Combine the fractions: $\frac{(9x + 15) - (8x - 12)}{12} = 3$ Simplify the numerator: $\frac{9x + 15 - 8x + 12}{12} = 3$ $\frac{x + 27}{12} = 3$

Step 3: Multiply both sides by 12 to eliminate the denominator: $x + 27 = 36$

Step 4: Solve for $x$: $x = 36 - 27$ $x = 9$

The solution to the equation is $x = 9$.

Would you like further details or help with any of these steps? Here are some related questions:

1. How do you find the least common denominator for two fractions?
2. What are the properties of equivalent fractions?
3. How can you simplify complex algebraic expressions?
4. How do you handle equations with fractions on both sides?
5. What are other methods to solve linear equations?

Tip: Always check your final answer by plugging it back into the original equation to ensure it satisfies the equation.