Which value below is a possible solution to the compound inequality
0<3x<30?
A. 5
B. 3.2
C. 45
D. -17
If you are substituting these number for x, then C and D do not apply; however, A and B both work. Is this how I should be doing it?
Unless you have a typo, I would agree that either A or B fits.
Yes, you are on the right track. To find the solution to the compound inequality 0 < 3x < 30, you need to find values of x that satisfy both inequalities.
First, let's divide the compound inequality 0 < 3x < 30 into two separate inequalities:
1. 0 < 3x
2. 3x < 30
To find the solution to each inequality, we need to isolate x.
For inequality 1, we divide both sides by 3 to isolate x:
0/3 < 3x/3
0 < x
This means x must be greater than zero.
For inequality 2, we divide both sides by 3 as well:
3x/3 < 30/3
x < 10
This means x must be less than 10.
Therefore, the values of x that satisfy both inequalities are:
0 < x < 10
Now let's check which of the given values, A. 5 or B. 3.2, fall within this range.
Using value A, 5, we can substitute it back into the compound inequality:
0 < 3(5) < 30
0 < 15 < 30
Both inequalities are true, so 5 is a possible solution.
Using value B, 3.2, we can do the same:
0 < 3(3.2) < 30
0 < 9.6 < 30
Again, both inequalities are true, so 3.2 is also a possible solution.
Therefore, both A. 5 and B. 3.2 are possible solutions to the compound inequality 0 < 3x < 30.