# How do you solve #abs(3x+5)-2x=3x+4#?

##### 1 Answer

#### Answer:

#### Explanation:

Start by isolating the modulus on one side of the equation

If you take into account the fact that the absolute value of a number, regardless if that number is positive or negative, is always **positive**

#color(blue)( |n| = {(n",", "if "n>=0), (-n",", "if "n<0) :})#

then you can say that the solutions to this equation must satisfy the condition

#5x+4>0 <=> x > -4/5#

Now, this equation can produce *two solutions*, depending on which condition is true

*If*#(3x+5)>0# ,*you have*

#|3x + 5| = 3x+5#

and the equation becomes

*If*#(3x+5)<0# ,*you have*

#|3x+5| = -(3x+5) = -3x-5#

This will get you

Since *extraneous*.

As a result, th only solution to this equation is