SOLUTION: solve |3-4x|=|x+5|

Question 821411: solve
|3-4x|=|x+5|
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Examine the equation according to four sets of conditions:
3-4x<0 and x+5<0;
3-4x>=0 and x+5<0;
3-4x>=0 and x+5>0;
3-4x<0 and x+5>=0.

Each of those sets of conditions will give you four different equations to solve. Put the entire set of solutions together.

You might want to check to see if any of the individual results does not work.

Note that for a real number k, if k>=0 then |k|=k; and if k<0 then |k|=-k. If this makes good sense to you, then you have the right idea about absolute value and you should have no trouble in handling these four equations. Think about this in relation to a number line.

and ;

and ;

and

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