I'll show you how to do one of the equations and one of the inequalities. All the others are done exactly in the same way: you'll only have to change the numbers, and it will be a good exercise.
Equations
Let's take the first equality as an example: we have
By definition, the absolute value of a number is the positive version of that number: if the number is already positive the absolute value doesn't change it; if a number is negative the absolute value changes its sign.
So, if the absolute value of a number is 5, than that number was already 5, or it was -5, and the absolute value changed it to positive 5.
So, the solutions are given by
Inequalities
Again, we'll use the first one as example. We have
By the same logic as before, the absolute value of a number is greater than 7 if the number is already greater than 7, or if it is smaller than -7. For example, we have |-10|=10>7.
So, we have
Instead, if we have an inequality with the "less than" sign, we have for example