Solutions for all numbers x ∈ R for the following equation?
The particular questions are:
∣x+3∣+∣5+4x∣=16
The particular questions are:
1 Answer
Answers are
Explanation:
We have two modulus monomials added to be equal
It means that for every single monomial we will have two options :
when the expression inside is positive and when it is negative.
It means that overall we will have four different cases:
- When
x+3>0and5+4x>0
so in this case, x has to be :x>−3andx>−54
What this means is that x should be x > -5/4
when you solve the equation for this these conditions, you get
You do in all cases the same process.
- (The second case ) you have
x+3>0and5+4x<0
when you solve
Two more cases you do on the same way.
You will get:
no solution
So the possible solutions are only
This can be done using graphical method also, but I prefer this one.