3|x-6| >= -2
Is this correct?
x>=16/3
x<=20/3
Think about it
|n| >= 0 for all n
so, |x-6| >= 0 for all x
any absolute value is >= -2
3|x-6| >= -2 for all values of x
So if the sign were to be <= then there is NO SOLUTION??
To determine if the answer is correct, let's solve the inequality step by step:
1. Start by isolating the absolute value expression:
3|x - 6| >= -2
2. Since any absolute value is always non-negative, we can ignore the negative sign on the right side of the inequality.
3|x - 6| >= 0
3. Divide both sides of the inequality by 3:
|x - 6| >= 0/3
|x - 6| >= 0
4. The absolute value of any number is always greater than or equal to 0. Therefore, this inequality holds true for all values of x.
5. There are no restrictions on the possible values of x. Hence, any real number is a valid solution for this inequality.
Therefore, the answer x >= 16/3 and x <= 20/3 is incorrect because it suggests there are specific constraints on the values of x, while in reality, there are none.