document.write( "Question 1119204: I kind of get that when you are solving an inequality like ∣5x+1∣>3 that you are supposed to do it in two cases. But, what I don't get is why one of those cases is 5x+1<−3 because I thought that absolute values can never be negative. Why do we do that case? \n" ); document.write( "
Algebra.Com's Answer #734674 by addingup(3677)\"\" \"About 
You can put this solution on YOUR website!
An absolute number cannot be negative. Pretend you are at the zero line and take two steps left, now you are standing on -2. Next I ask you to go back to the zero line and take two steps right. Now you're standing on the +2. But both times you took two steps. Absolute value doesn't care about the direction, only about the distance.
\n" ); document.write( "To solve your equation:
\n" ); document.write( "∣5x+1∣>3 to solve, we rewrite:\r
\n" ); document.write( "\n" ); document.write( "5x+1>3 subtract 1 on both sides
\n" ); document.write( "5x > 2 divide both sides by 5
\n" ); document.write( "x > 2/5 so your yardstick is 2/5 to the right, in the positive. And how far does it go to the left, to the negative? Because the answer will let you calculate the length of your yardstick
\n" ); document.write( "5x+1>-3
\n" ); document.write( "5x>-4
\n" ); document.write( "x<-4/5 (notice the change in the direction of the sign because, from zero, we are decreasing 4/5)
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\n" ); document.write( "So, how long is your yardstick? It goes from -4/5 on the left to 2/5 on the right:
\n" ); document.write( "2/5--4/5 = 6/5 = 1.2 This is how long your yardstick is.\r
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