The response from the other tutor shows a perfectly good standard formal algebraic solution.
A very different method for solving the problem is often much easier than the standard algebraic method.
The expression can be interpreted as saying the difference between x and a is equal to b. For example, means the difference between x and 5 is 3; that means x is either 5+3=8 or 5-3=2.
We can solve this problem using that method.
Divide everything by 2, because we need "x" to be by itself:
This absolute value inequality says that the difference between x and 1.5 is greater than or equal to 0.5.
1.5-0.5=1, so the difference between x and 1.5 is greater than or equal to 0.5 if x is less than or equal to 1;
1.5+0.5=2, so the difference between x and 1.5 is greater than or equal to 0.5 if x is greater than or equal to 2
So the inequality is satisfied if x is either less than or equal to 1, or greater than or equal to 2.
