please check answers and change if wrong thank you.
The absolute value of 3 times a number x is greater than 33.
|3x| > 33
3x > 33
x > 11
what about -11
good question.
|x| = x if x>=0
So, your answer of 11 correctly solves
3x > 33
But, |x| = -x if x < 0
so, the other condition is
-3x > 33
x < -11
So, if x is farther than 11 units from 0, in either direction, 3x is farther than 33 units away from 0.
thank you very much for your help, anonymous. thanks ann
To find the absolute value of -11, you can take the number without its sign. So, the absolute value of -11 is 11.
To address the inequality |3x| > 33, you need to consider both positive and negative solutions for x.
For the positive solution:
We start with the inequality 3x > 33. To isolate x, divide both sides of the inequality by 3: x > 11.
For the negative solution:
To consider the negative solution, we need to consider the absolute value of -3x as well. The inequality becomes |-3x| > 33. By applying the same steps as before, we have -3x > 33. Divide both sides by -3, remembering to reverse the inequality sign when dividing by a negative number: x < -11.
So, the solutions to |3x| > 33 are x > 11 and x < -11.