x + 3|x| = 10. Find the value of x

Solution:

The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x.

Case 1: When 'x' is positive.

|x| = x

Therefore,

x + 3|x| = 10

⇒ x + 3x = 10

⇒ 4x = 10

⇒ x = 10/4

⇒ x = 2.5

Case 2: When 'x' is negative.

|-x| = x

Thus,

x + 3|x| = 10

⇒ -x + 3|-x| = 10

⇒ -x + 3x = 10

⇒ 2x = 10

⇒ x = 5

Thus, for the equation, x + 3|x| = 10, the values of 'x' will be 2.5 when 'x' is positive and 5 when 'x' is negative.

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x + 3|x| = 10. Find the value of x

Summary:

For the equation x + 3|x| = 10, the values of 'x' will be 2.5 when 'x' is positive and 5 when 'x' is negative.