solve the inequality: 3|m-4|>6
A. [m|2<m<6]
B. [m|<2 or m>6]
C. [m|m<1 or m>7]
D. all real numbers
anyonee??
3|m-4|>6
|m-4|>2
m-4 > 2 or -m+4 > 2
m > 6 or -m > -2
m > 6 or m < 2
m < 2 OR m > 6 , looks like B)
thanks
To solve the inequality 3|m-4| > 6, we can break it down into two cases:
Case 1: (m - 4) is negative or zero
In this case, |m-4| = -(m-4), and the inequality becomes: 3(-(m-4)) > 6.
Simplifying this, we get: -3m + 12 > 6.
Subtracting 12 from both sides, we have: -3m > -6.
Dividing both sides by -3, we get: m < 2.
Case 2: (m - 4) is positive
In this case, |m-4| = (m-4), and the inequality becomes: 3(m-4) > 6.
Simplifying this, we get: 3m - 12 > 6.
Adding 12 to both sides, we have: 3m > 18.
Dividing both sides by 3, we get: m > 6.
Putting the results from both cases together, we have the solution: m < 2 or m > 6.
Therefore, the correct answer is B. [m|<2 or m>6].