The smallest real number in the solution set of 2x > 6 is 4.
A) True
B) False - The smallest real number in the solution set of 2x > 6 is 3.
C) False - The smallest real number in the solution set of 2x > 6 is a number greater than 3. For example, 3.01 is a real number that is in the solution set.
2x > 6
x > 3
4 would be the smallest integer solution, but there is no "smallest real number" such that x > 3
If you claim you have the smallest number > 3 ,
then I will take the average of your number and 3 and it will be smaller.
To solve the inequality 2x > 6, we need to isolate the variable x.
First, subtract 6 from both sides of the inequality: 2x - 6 > 0.
Then, divide both sides of the inequality by 2: (2x - 6)/2 > 0/2, which simplifies to x - 3 > 0.
Now, we can solve this inequality for x. To determine the smallest real number in the solution set, we can analyze the inequality to find the critical points.
The critical point of an inequality in the form x - a > 0 is a. In this case, the critical point is 3 because x - 3 > 0.
To find the solution set, we can set up a number line. On the number line, plot the critical point at 3 and consider a test point before and after that to determine whether it satisfies the inequality.
If we choose the number 2 as our test point, we can substitute it into the inequality: 2 - 3 > 0, which simplifies to -1 > 0. Since -1 is not greater than 0, it does not satisfy the inequality.
If we choose the number 4 as our test point, we can substitute it into the inequality: 4 - 3 > 0, which simplifies to 1 > 0. Since 1 is greater than 0, it satisfies the inequality.
Therefore, the solution set is x > 3, where x is a real number greater than 3.
Looking at the options:
A) True - The statement "The smallest real number in the solution set of 2x > 6 is 4" is incorrect based on our analysis.
B) False - The statement "The smallest real number in the solution set of 2x > 6 is 3" is correct based on our analysis.
C) False - The statement "The smallest real number in the solution set of 2x > 6 is a number greater than 3" is incorrect. The smallest real number in the solution set is indeed 3.
Therefore, the correct answer is B) False - The smallest real number in the solution set of 2x > 6 is 3.