Answer
The two solutions to this inequality are
x ≤ 0
OR
x ≥ 1
The graph is attached below
Step-by-step explanation
We are told to solve the inequality equation given and plot the graph of the solution set
x² ≥ x
x² - x ≥ 0
x (x - 1) ≥ 0
At this point, the solution set if this was a normal equation would be
x (x - 1) = 0
x = 0 or x - 1 = 0
x = 0 or x = 1
So, the possible solution sets include
x ≤ 0
0 ≤ x ≤ 1
x ≥ 1
And the equation is that
x (x - 1) ≥ 0
If x ≤ 0, let x = -1
x (x - 1) = -1 (-1 -1) = -1 (-2) = 2 ≥ 0
Hence, x ≤ 0 is a solution
If 0 ≤ x ≤ 1, let x = 0.5
x (x - 1) = 0.5 (0.5 -1 ) = 0.5 (-0.5) = -0.25 not ≥ 0
Hence, 0 ≤ x ≤ 1 is not a solution
If x ≥ 1, let x = 2
x (x - 1) = 2 (2 -1 ) = 2 (1) = 2 ≥ 0
Hence, x ≥ 1 is a solution
So, the two solutions to this inequality are
x ≤ 0
OR
x ≥ 1
To plot the graph now,
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
And, x ≤ 0 means the wanted region is the region from x = 0 to all the numbers less than 0.
x ≥ 1 means the wanted region is the region from x = 1 to all the numbers greater than 1.
The graph of this solution set is attached under 'Answer'
Hope this Helps!!!