use interval notation to express the solution set of the inequality |2x + 3|> or equal to 9
|2x + 3| ≥ 9
then
2x+3 ≥ 9 OR -2x-3 ≥ 9
2x ≥ 6 or -2 ≥ 12
x ≥ 3 or x ≤ -6
I will leave it up to you to put that in the interval notation. We used the above notation in my days.
To express the solution set of the inequality |2x + 3| ≥ 9 using interval notation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2x + 3 ≥ 0
In this case, we can simply remove the absolute value and solve for x:
2x + 3 ≥ 9
Subtract 3 from both sides:
2x ≥ 6
Divide both sides by 2:
x ≥ 3
Case 2: 2x + 3 < 0
In this case, we need to change the direction of the inequality and also remove the absolute value:
-(2x + 3) ≥ 9
Distribute the negative sign:
-2x - 3 ≥ 9
Subtract 3 from both sides:
-2x ≥ 12
Divide both sides by -2, but remember when dividing by a negative number, the direction of the inequality flips:
x ≤ -6
Now, we can combine the two cases using interval notation.
When 2x + 3 ≥ 0 (Case 1), the solution set is x ≥ 3, which can be written as: [3, +∞)
When 2x + 3 < 0 (Case 2), the solution set is x ≤ -6, which can be written as: (-∞, -6]
Therefore, the solution set of the inequality |2x + 3| ≥ 9 using interval notation is (-∞, -6] ∪ [3, +∞).