Option A (uppermost number line) represents the solution set to inequality |2 · x - 6| < 4.
What number line does belong to a given inequality?
In this question we must determine what number line corresponds with inequality |2 · x - 6| < 4. This can done by finding the solution set by definition of absolute value and algebra properties:
By definition of absolute value:
- 4 < 2 · x - 6 < 4
Second, by algebra properties:
2 · x - 6 > - 4 and 2 · x - 6 < 4
2 · x > 2 and 2 · x < 10
x > 1 and x < 5
Then, by direct inspection, we find that right choice is option A.