The image you've uploaded shows Question 7, which asks you to solve the equation:

$|2x - 1| = 7$

To solve this absolute value equation, we need to consider two cases because the absolute value expression $|2x - 1|$ can be either positive or negative:

Case 1:

$2x - 1 = 7$

Solving for $x$:

$2x = 7 + 1$

$2x = 8$

$x = 4$

Case 2:

$2x - 1 = -7$

Solving for $x$:

$2x = -7 + 1$

$2x = -6$

$x = -3$

So, the solutions to the equation are $x = 4$ and $x = -3$.

Would you like further details or have any questions? Here are five related questions:

1. How can you verify if your solutions are correct in an absolute value equation?
2. What is the general approach to solving absolute value equations?
3. Can absolute value equations have no solution? If so, under what conditions?
4. What is the difference between an absolute value equation and an absolute value inequality?
5. How would the solutions change if the absolute value equation was $|2x - 1| = -7$?

Tip: Always remember that the absolute value of a number is always non-negative. This can help you quickly identify if an equation has no solution.