Question

Find the inequality that creates the following graph

Answer 1

|2x - 3| ≥ 1

Explanation:

Since the absolute value function is always ≥ 0 we can conclude that
|2x - 3| ≥ 0 so we can eliminate choices 2 and 4

That leaves two possibilities:
|2x - 3| ≥ 1 and |2x - 3| ≤ 1

There are two ways to go about solving this

Pick a point in the given graph on each side of the segment marked in red and see which of the two inequalities both points satisfy

Two points which are on both segments are x = 0 and x = 1

Plug x = 0 into |2x - 3|
|2x - 3| at x = 0
=> | 2 ·0 - 3|
=> |0 - 3|
=> |-3|
= 3

Since 3 ≥ 1, point x = 0 satisfies |2x - 3| ≥ 1

But it does not satisfies |2x - 3| ≤ 1 since 3 is not less than or equal to 1

So the correct inequality is |2x - 3| ≥ 1