s the following always, sometimes, or never true?
2(3π₯ β 1) + 4 > 6π₯ + 2
a) Always true
b) Sometimes true
c) Never true
b) Sometimes true
To determine if the inequality 2(3π₯ β 1) + 4 > 6π₯ + 2 is always, sometimes, or never true, we need to solve it.
First, we simplify both sides of the inequality:
2(3π₯ β 1) + 4 > 6π₯ + 2
6π₯ β 2 + 4 > 6π₯ + 2
6π₯ + 2 > 6π₯ + 2
Next, we can see that the 6π₯ terms cancel out on both sides:
2 > 2
This equation is always true.
Therefore, the answer is: a) Always true.
In order to determine whether the inequality 2(3π₯ β 1) + 4 > 6π₯ + 2 is always, sometimes, or never true, we need to solve it and analyze the solution.
First, let's simplify the inequality:
2(3π₯ β 1) + 4 > 6π₯ + 2
6π₯ β 2 + 4 > 6π₯ + 2
6π₯ + 2 > 6π₯ + 2
Simplifying further,
6π₯ > 6π₯
As we can see, the expression "6π₯ > 6π₯" is always true, regardless of the value of π₯. In other words, any value of π₯ would satisfy the inequality.
So, the correct answer is: a) Always true.