document.write( "Question 581129: Hi. I would like to know about this problem. -8x+3 greater than or equal to 27. Thank you. \n" ); document.write( "

Algebra.Com's Answer #371491 by KMST(5328) $\"\"$ $\"About$

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$\"-8x%2B3%3E=27\"$
\n" ); document.write( "Adding (-3) to both sides (or subtracting 3 from both sides), the greater than or equal relationship is still true, so
\n" ); document.write( " $\"-8x%3E=27-3\"$ --> $\"-8x%3E=24\"$
\n" ); document.write( "Multiplying (or dividing) both sides by a positive number maintains the inequality relationship, but multiplying (or dividing) both sides by a negative number reverses it. If we multiply both sides by $\"-1%2F8\"$ (or divide both sides by $\"-8\"$ ),
\n" ); document.write( " $\"-8x%3E=24\"$ transforms into the equivalent $\"%28%28-8%29%2F%28-8%29%29%2Ax%3C=24%2F%28-8%29\"$
\n" ); document.write( "That $\"%28%28-8%29%2F%28-8%29%29\"$ is optional, of course.
\n" ); document.write( "You could write $\"x%3C=24%2F%28-8%29\"$ and no one should object.
\n" ); document.write( "Then you just do the $\"24%2F%28-8%29\"$ division and end up with
\n" ); document.write( " $\"highlight%28x%3C=-3%29\"$
\n" ); document.write( "You can verify by seeing, for example, that x=-3, and x=-4 are solutions of the original inequality, but x=0 is not.
\n" ); document.write( "If multiplying by negative numbers when solving inequalities makes you nervous, you can go the long way around it, just adding stuff and only multiplying/dividing by positive numbers, like this
\n" ); document.write( " $\"-8x%3E=24\"$ --> $\"-8x%2B8x%3E=24%2B8x\"$ --> $\"0%3E=24%2B8x\"$ --> $\"0-24%3E=24%2B8x-24\"$ --> $\"-24%3E=8x\"$ --> $\"-24%2F8%3E=8x%2F8\"$ --> $\"-3%3E=x\"$ \n" ); document.write( "

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