How to solve 4|x+3|-7=5 algebraiclly

Question

Absolute value 

Answer 1

To solve problems with absolute value, you need to get the absolute value part by itself.  Here's the steps:

 

4 |x+3| = 12  (add 7 to both sides)

 

|x+3| = 3 (divided both sides by 4)

 

Now that the absolute value part is by itself, you set up two equations.  The first one is you pretend there's no absolute value signs, which gives you:

 

x+3 = 3

x=0 (subtracted 3 from both sides)

 

The other equation is you drop the absolute value signs and make the right side of the equation negative.  This gives you:

 

x+3 = -3

x = -6 (subtracted 3 from both sides again)

 

So, your two answers are 0 and -6.  Be careful when doing absolute value, though.  If you get the absolute value part by itself and it's equal to a negative number, there's no solution (absolute values are always positive) so no need to set up two equations.