Let's analyze and solve the requested questions 7 and 8 from the image.

Question 7:

Simplify the expression $\frac{3x - 3}{2x - 4} = 5$

Solution:

1. Start by isolating the fraction on one side: $\frac{3x - 3}{2x - 4} = 5$

2. Multiply both sides by $(2x - 4)$ to eliminate the denominator: $3x - 3 = 5(2x - 4)$

3. Distribute the $5$ on the right side: $3x - 3 = 10x - 20$

4. Get all the $x$ terms on one side and the constant terms on the other: $3x - 10x = -20 + 3$ $-7x = -17$

5. Divide by $-7$ to solve for $x$: $x = \frac{17}{7}$

So, the solution is: $x = \frac{17}{7}$

Question 8:

Find the equation of Line N as shown in the graph.

Solution:

1. The graph shows a line intersecting at two points: (2, 4) and (0, 6).

2. First, calculate the slope $m$ using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 4}{0 - 2} = \frac{2}{-2} = -1$

3. Now use the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Since the line passes through (0, 6), the y-intercept $b = 6$.

4. The equation of the line is: $y = -x + 6$

So, the equation of Line N is: $y = -x + 6$

Would you like further details on these solutions or have any additional questions? Here are five related questions you might find useful:

1. How do you solve a similar equation involving fractions and variables?
2. How do you find the slope of a line if given different points?
3. What does the slope-intercept form of a line represent graphically?
4. How can you check the correctness of a calculated slope or y-intercept?
5. What are other forms of linear equations apart from slope-intercept form?

Tip: Always cross-check by substituting your solution back into the original equation to verify its correctness.