SOLUTION: Please help me to figure out if there is no solution one solution or infinite solutions to the following problems. 3x-1<24 and x-3<8

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Question 875257: Please help me to figure out if there is no solution one solution or infinite solutions to the following problems. 3x-1<24 and x-3<8
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That kind of problem always has infinite solutions.
3x-1 and x-3 are linear expressions in x .
As x increases the value of those expressions increases.
As x decreases the value of those expressions decreases.

3x-1%3C24
If you find that for some x , say x=8 ,
the value of 3x-1 is less than 24 ,
then any other smaller x will also be a solution.
3%2A8-1=24-1=23%3C24 so x=8 is a solution,
but so is any number smaller than 8,
such as -1000, -3%2F5 , %220%22 , 1, sqrt%282%29 , pi .
There are infinite solutions, so we cannot list them all.
We have to give a formula (an inequality) that shows all the solutions
3x-1%3C24 --> 3x-1%2B1%3C24%2B1 --> 3x%3C25 --> 3x%2F3%3C25%2F3 --> highlight%28x%3C35%2F3%29
Since 25%2F3=8%261%2F3 , that can also be written as highlight%28x%3C8%261%2F3%29

x-3%3C8 --> x-3%2B3%3C8%2B3 --> highlight%28x%3C11%29
Some of the infinite solutions are 10.999 , 1, -1%2F2 ,
and many other numbers that are less than 11.