document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #528108 by KMST(5328) $\"\"$ $\"About$

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That kind of problem always has infinite solutions.
\n" ); document.write( " $\"3x-1\"$ and $\"x-3\"$ are linear expressions in $\"x\"$ .
\n" ); document.write( "As $\"x\"$ increases the value of those expressions increases.
\n" ); document.write( "As $\"x\"$ decreases the value of those expressions decreases.
\n" ); document.write( "
\n" ); document.write( " $\"3x-1%3C24\"$
\n" ); document.write( "If you find that for some $\"x\"$ , say $\"x=8\"$ ,
\n" ); document.write( "the value of $\"3x-1\"$ is less than $\"24\"$ ,
\n" ); document.write( "then any other smaller x will also be a solution.
\n" ); document.write( " $\"3%2A8-1=24-1=23%3C24\"$ so $\"x=8\"$ is a solution,
\n" ); document.write( "but so is any number smaller than $\"8\"$ ,
\n" ); document.write( "such as $\"-1000\"$ , $\"-3%2F5\"$ , $\"%220%22\"$ , $\"1\"$ , $\"sqrt%282%29\"$ , $\"pi\"$ .
\n" ); document.write( "There are infinite solutions, so we cannot list them all.
\n" ); document.write( "We have to give a formula (an inequality) that shows all the solutions
\n" ); document.write( " $\"3x-1%3C24\"$ --> $\"3x-1%2B1%3C24%2B1\"$ --> $\"3x%3C25\"$ --> $\"3x%2F3%3C25%2F3\"$ --> $\"highlight%28x%3C35%2F3%29\"$
\n" ); document.write( "Since $\"25%2F3=8%261%2F3\"$ , that can also be written as $\"highlight%28x%3C8%261%2F3%29\"$
\n" ); document.write( "
\n" ); document.write( " $\"x-3%3C8\"$ --> $\"x-3%2B3%3C8%2B3\"$ --> $\"highlight%28x%3C11%29\"$
\n" ); document.write( "Some of the infinite solutions are $\"10.999\"$ , $\"1\"$ , $\"-1%2F2\"$ ,
\n" ); document.write( "and many other numbers that are less than 11. \n" ); document.write( "

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