SOLUTION: My question is how to solve: 2x+1<3x<12

Question 71920: My question is how to solve:
2x+1<3x<12

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
2x+1<3x<12
.
Split this into two problems. The first problem is
.
2x + 1 < 3x
.
Subtract 2x from both sides and you get:
.
+1 < x
.
This tells you that x must be greater than +1.
.
Now let's work the second problem. It is:
.
3x < 12
.
Dividing both sides by +3 results in:
.
x < +4
.
So on one hand, x must be greater than +1, but on the other hand x must be less than +4.
We can write this as:
.
+1 < x < +4
.
As a check you can select some values of x between +1 and +4 and plug them in to the original
problem. For example, let's try x = +2. Using this value, the original problem becomes:
.
2x + 1 < 3x < 12
.
2(+2) + 1 < 3(+2) < 12
.
4 + 1 < 6 < 12
.
5 < 6 < 12
.
That works ... so x = +2 works as a check.
.
Hope this helps you understand how to work the problem.
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