The solution for the absolute value equations are:
|4 - y| = 1 ---> x = 3 and x = 5
|3x| = 9 ---> x = 3 and x = -3
|2x + 7| = 9 ---> x = 2 and x = -8
How to solve the absolute value equations?
Remember that the absolute value function works as follows:
|x| = x if x ≥ 0
|x| = -x if x < 0.
So, for the first equation:
|4 - y| = 1
We can break it into two equations:
(4 - y) = 1 ----> y = 4 - 1 = 3
(4 - y) = -1 ----> y = 4 + 1 = 5
For the next equation we have:
|3x| = 9
Again, break this into two equations:
3x = 9
3x = -9
Solving both for x:
x = 9/3 = 3
x = -9/3 = -3
The next one is:
|2x + 7| = 9
Breaking the absolute value we get:
2x + 7 = 9
2x + 7 = -9
Solving these two we get:
x = (9 - 7)/2 = 2
x = (-9 - 7)/2 = -8
And so on.