- #1
solar nebula
- 14
- 0
Homework Statement
So this is the question
|x-1|+|x-2|>1
Homework Equations
N/A
The Attempt at a Solution
I tried it, the solution seems right, but i don't know if my approach is correct.
The first step is to isolate the absolute value expression by itself on one side of the inequality. This can be done by using inverse operations, such as addition or subtraction, to move any other terms to the other side of the inequality.
The critical values in an absolute value inequality are the points where the absolute value expression equals 0. In this case, the critical values are x = 1 and x = 2, since these are the points where |x-1| and |x-2| equal 0, respectively.
The critical values act as boundaries for the solution set of the inequality. Any values of x that fall between the critical values will satisfy the inequality, while any values outside of the critical values will not. In other words, the critical values help us determine which parts of the number line to include in our solution set.
In this case, we can break the inequality into two separate inequalities, one for each absolute value expression. This allows us to find two different solution sets, which we can then combine to find the final solution set for the original inequality.
The solution set for an absolute value inequality can be represented on a number line by shading in the appropriate regions between the critical values. In this case, we would shade in the region between 1 and 2, as well as any values greater than 2 or less than 1. This represents all the values of x that satisfy the given inequality.