Absolute value equation

Question

Enter your answers and any extraneous solutions as comma-separated list of values or enter none if none exist

x|x-7|=47x+7

Answer 1

Step 1:

The absolute equation is .

Rewrite the absolute equation,

Solve the equations.

(i)

Since the roots are irrational roots.

Hence, Quadratic equation roots formula is

Substitute in the above formula.

(ii)

Since the roots are irrational roots.

Hence, Quadratic equation roots formula is

Solution:

The solutions are,

Comments

What are the valid solutions and extraneous solutions of x?

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The valid solutions are

The extraneous solution