Write the solution set of /x-3/>5 in set builder notation

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll have to solve the double inequality:

-5>x-3>5

We'll solve the first, left, inequality and we'll apply the symmetric formula:

x - 3 < -5

We'll add 3 both sides:

x < -5 + 3

x < -2

x belongs to the interval of values: (-infinite, -2)

We'll solve the right inequality:

x - 3 > 5

We'll add 3 both sides:

x > 5 + 3

x > 8

x belongs to the interval (8, +infinite).

The common solution of the system is the empty set since there is no value for x to satisfy both inequalities at the same time.

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