<p>How do you solve this kind of question:</p>
<p>[3x-5] < 6</p>
<p>[] = absolute value</p>
<p>I thought it was supposed to be two equations, like this:</p>
<p>3x-5 < 6
3x-5 > -6</p>
<p>BUT, my math book says that this is incorrect. Help?</p>
<p>I think the less than and greater than signs shouldn’t be switched unless you are dividing by a negative number. You would solve like this 3x-5<6 or 3x-5<-6
3x<11 or 3x<-1
3x/3<11/3 or 3x/3<-1/3
X<11/3 or X<-1/2</p>
<p>These are the two equations you use:
3x - 5 < 6
-3x + 5 < 6</p>
<p>One is the original equation without the absolute value function, the second also has no absolute value function, but everything that was in the absolute value function is multiplied by -1 (because the absolute value function outputs the same value for A and -A)</p>
<p>3x - 5 < 6
3x < 11
x < 11/3</p>
<p>-3x + 5 < 6
5 < 6 + 3x
-1 < 3x
-1/3 < x</p>
<p>So -1/3 < x < 11/3</p>
<p>The above method works in this case too, but I think it can get wonky if you have variables on the right hand side. Could be wrong.</p>
<p>|3x-5| < 6</p>
<p>-6 < 3x-5 < 6</p>
<p>Add 5:</p>
<p>-1 < 3x <11</p>
<p>Divide by 3:</p>
<p>-1/3 < x < 11/3</p>
<p>Just remember that if |x| is less than something, it has to be between two numbers.
If |x| is greater, it is an “or” equation.</p>
<p>Remember: Less thAND, GreatOR</p>