document.write( "Question 262405: I need help with INDIRECT PROOFS.
\n" ); document.write( "Given: -4x + 2 <-10
\n" ); document.write( "Prove: x > 3
\n" ); document.write( "All I know is that you have to do the opposite which would be -4x + 2 is greater than or equal to -10. That is as far as I have gotten and I do not know where to go from there. \n" ); document.write( "
Algebra.Com's Answer #193328 by drk(1908)\"\" \"About 
You can put this solution on YOUR website!
The basic goal of indirect proofs is you assume the opposite of what you are trying to prove as true and try to get some kind of contradiction. Lets see where this takes us . . .
\n" ); document.write( "STATEMENT #1: x <= 3
\n" ); document.write( "REASON #1: indirect assumption
\n" ); document.write( "STATEMENT #2: -4X + 2 < -10
\n" ); document.write( "REASON #2: Given
\n" ); document.write( "STATEMENT #3: -4x + 2 - 2 < -10 - 2
\n" ); document.write( "REASON #3: subtraction property of equality
\n" ); document.write( "STATEMENT #4: -4x < -12
\n" ); document.write( "REASON #4:additive inverse property
\n" ); document.write( "STATEMENT #5: -4x* (-1/4) > -12 * (-1/4)
\n" ); document.write( "REASON #5:multiplication property of equality
\n" ); document.write( "STATEMENT #6: x > 3
\n" ); document.write( "REASON #6:multiplicative inverse property
\n" ); document.write( "Notice we have a contradiction between step #1 and step #6. Since we have a contradiction, our assumption of statement #1 was false and therefore,
\n" ); document.write( "x > 3. \n" ); document.write( "
\n" );