Question

What do you do when you have absolute values on both sides of the equations?

Answer 1

Explanation:

When we have absolute values on both sides of the equations,

we must consider both possibilities for acceptable solutions - positive and negative absolute valueexpressions.

We will look at an example first to understand:

Example-1

Solve for x:

|2x−1|=|4x+9|

Both sides of the equation contain absolute values.

Find solutions as shown below:

(2x−1)=−(4x+9) .. Exp.1

OR

(2x−1)=(4x+9) ...Exp.2

Case.1:

Consider ... Exp.1 first and solve for x

(2x−1)=−(4x+9)

⇒2x−1=−4x−9

Add 4x to both sides of the equation.

⇒2x−1+4x=−4x−9+4x

⇒2x−1+4x=−4x−9+4x

⇒6x−1=−9

Add 1 to both sides of the equation.

⇒6x−1+1=−9+1

⇒6x−1+1=