# How do you solve #|\frac { 7x - 3} { 5} | = 3#?

##### 1 Answer

#### Explanation:

Absolute value problems can be confusing. Some teachers say "they make numbers positive," but that's only partially correct. Absolute value functions measure distance. That means, if you stand at point **OR**

Let's make two equations right now:

We need to solve for two possibilities, one where the function is negative and one where it's negative:

**Positive**

**Negative**

Now we need to solve both of these:

*multiply by #5# on both sides*

*add #3# on both sides*

*divide by #7#*

Now for the other one:

*multiply by #-1# on both sides*

*multiply by #5# on both sides*

*add #3# on both sides*

*divide by #7# on both sides*

Those are our solutions.

Just to check, let's graph our equation and see if our roots match:

graph{abs((7x-3)/5)-3}

Those are the decimal approximation of our fractions! We're right