Let's solve the problems shown in the image one by one.

Problem 5:

$6 - 5x = 1 - 4x$

• Move all the $x$-terms to one side and the constants to the other side. $6 - 1 = 5x - 4x$ $5 = x$ So, the solution is: $x = 5$

Problem 7:

$16 - 3 + 7x - 3x = 6x - 1$

• First, simplify both sides: $13 + 4x = 6x - 1$
• Move all $x$-terms to one side and the constants to the other: $13 + 1 = 6x - 4x$ $14 = 2x$ $x = \frac{14}{2} = 7$ So, the solution is: $x = 7$

Problem 9:

$r + 3 + 4 + 11 = -r - 4r$

• Simplify both sides: $r + 18 = -5r$
• Move all $r$-terms to one side: $r + 5r = -18$ $6r = -18$ $r = \frac{-18}{6} = -3$ So, the solution is: $r = -3$

Do you want further details or have any questions on these solutions?

Here are five related questions to explore further:

1. How can you check if your solution is correct for each equation?
2. What are common errors when solving linear equations?
3. How do you handle equations with variables on both sides?
4. How do you graph solutions to linear equations?
5. How can you solve more complex equations, such as quadratic or cubic equations?

Tip: When solving linear equations, always simplify both sides fully before isolating the variable.