Maths-

General

Easy

Question

# Yumiko solved . Explain the error Yumiko made ?

Hint:

### |x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

So, we will get two cases in the solution of the given inequality. We will see that the solution is different that of Yumiko.

## The correct answer is: This solution can only be received only if the given equation is |x| < 5

### Step by step solution:

The given inequality is

|x| > 5

Using the definition,

We get two cases

For x < 0,

We have

|x| = -x > 5

Multiplying -1 throughout,

x < -5

For x ≥ 0, we have

|x| = x > 5

that is

x > 5

Combining the two solutions, we get

x < -5 and x > 5

Whereas Yumiko’s solution is

x > -5 and x < 5

Which is completely wrong.

This solution can only be received only if the given equation is

|x| < 5

Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.

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