# Question #c041e

##### 2 Answers

#### Explanation:

Right from the start, the fact that you're dealing with the **absolute value** of an expression tells you that **must be**

That is the case because *regardless* of the sign of the expression inside the absolute value signs, the expression on the right side of the equation **must** be greater than or equal to

Since you have

#|5x + 8| = x#

you can say that **must** return a value that is

So, you know that you have two possible scenarios to look at

#5x + 8 >= 0 implies |5x + 8| = 5x + 8# In this case, you have

#5x + 8 = x#

#4x = -8 implies x = (-8)/4 = -2#

#5x +8 < 0 implies |5x +8| = - (5x+8)# In this case, you have

#-(5x + 8) = x#

#-5x - 8 = x#

#-6x = 8 implies x= 8/(-6) = -4/3#

However, you already know that you need

#x >=0#

so you can say that **will not** be valid solutions to the original equation.

This means that the original equation has **no solution** when working with real numbers, or

Simpler and Quicker version of the same thing.

#### Explanation:

The solutions, if any exist, are found by solving the equations

These are simple linear equations.

The first yields

This cannot be a solution since x must be positive.

The second equation yields

This cannot be a solution since x must be positive.

The solution set is {}.