# How do you solve and check for extraneous solutions in #sqrt(3x - 2) + 3 =4x#?

##### 1 Answer

#### Answer:

#### Explanation:

Start by isolating the radical term on one side of the equation. This can be done by adding

Now, because you can't take the squaree root of a negative number if you're working with *real numbers*, any solution you will find must satisfy two conditions

#3x-2>=0 implies x >=2/3# #4x-3 >=0 implies x >=3/4#

Overall, you need

Square both sides of the equation to remove the radical term

Rerarrange to get

Use the *quadratic formula* to find the two solutions to this quadratic equation

Notice that only *extraneous solution*.

This is of course because

Therefore, your original equation will only have one solution,

Do a quick check to make sure that the calculations are corret