Answer:
To solve this inequality, you can start by isolating the absolute value term on one side of the inequality. To do this, you can subtract 9x from both sides, which gives you:
|9x| - 9x ≥ 27 - 9x
|9x| - 9x ≥ -9x
Next, you can apply the properties of absolute values to simplify the expression. The absolute value of a number is always positive, so the absolute value of any expression will be equal to the expression itself if it is positive, and equal to the negative of the expression if it is negative.
Since the inequality is "greater than or equal to," you need to consider both cases.
If 9x is positive:
9x - 9x ≥ -9x
0 ≥ -9x
x ≤ 0
If 9x is negative:
-9x - 9x ≥ -9x
-18x ≥ -9x
-9x ≥ 0
x ≤ 0
In both cases, the solution is x ≤ 0. This means that any value of x that is less than or equal to 0 will satisfy the inequality.
To write this solution in interval notation, you can use the notation [0,∞) to represent all values of x that are greater than or equal to 0. Alternatively, you can use the notation (-∞,0] to represent all values of x that are less than or equal to 0.
Explanation: