What are integer elements of set B is they have the property |x-2|<3?

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beckden's profile pic

beckden | High School Teacher | (Level 1) Educator

Posted on

if |a|<b  then a>-b or a<b.

So

|x-2|<3 gives us x-2>-3 and x-2<3

Solving we get x>-1 and x<5

The only integers which are >-1 and <5 is 0, 1, 2, 3, and 4.

So our answer is B = {0,1,2,3,4}

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To discover the elements of the set, we'll have to solve the inequality. We'll recall the property of absolute value:

|x|<c <=> -c < x < c

According to this property, we'll have:

-3 < x - 2 < 3

We'll solve the left inequality:

-3 < x - 2

We'll isolate x to the right:

-3 + 2 < x

-1 < x

We'll solve the right inequality:

x - 2< 3

x < 3 + 2

x < 5

The integer element located between -1 and 5, except the values -1 and 5, are: {0 , 1 , 2 , 3 , 4}.

Therefore, the elements of the set B, whose property is |x - 2|<  3 are {0 , 1 , 2 , 3 , 4}.

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