mathFind the integers x if |x-2|=<3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have the inequality |x-2|=<3.

The modulus sign gives us two equivalent inequalities.

-3 =< (x - 2) =< 3

-3 =< (x - 2)

=> -1 =< x

(x - 2) =< 3

=> x =< 5

The integers that x can take on are (-1 , 0, 1, 2, 3, 4 , 5)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

From enunciation, we'll have to find out the integer elements that satisfy the inequality |x-2|=<3.

We'll re-write the constraint |x-2|=<3:

-3=< x-2 =<3

We'll solve the left side of the inequality:

-3 =< x-2

We'll add 3 both sides:

0 =<x - 2 + 3

0 =< x + 1

We'll subtract 1 both sides:

-1 =< x

Now, we'll solve the right side:

x - 2 =< 3

We'll add 2 both sides, to isolate x:

x =< 5

So, from both inequalities, we'll get: -1 =< x =< 5

The integer elements of the set are:{-1 ; 0 ; 1 ; 2 ; 3 ; 4 ; 5}.

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