Question

How do you solve `|3b - 3| \leq 12`?

Answer 1

`-3<=b<=5`

Explanation:

Consider these condition:

`|-13|=+13 >12`

From this scenario we can deduce you may not have any value of `3b-3` that is less than `-12`

In the same way we may not have any value of `3b-3` that is greater than +12

Consider these points as limiting the range such that we have:

`-12<=3b-3<=12`

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Consider the lower bound (-12)

Set `" "3b-3=-12color(white)("ddd") =>color(white)("ddd") b=(3-12)/3=-3`

So `color(white)("dd")3b-3>=-12color(white)("ddd")=>color(white)("dddd")b>=(3-12)/3`

`color(white)("ddddddddddddddddddd")=>color(white)("dddd")b>=-3`

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Consider the upper bound (+12)

Set`color(white)("d")3b-3=+12color(white)("dddd")=>color(white)("dddd")b=(12+3)/3=+5`

So`color(white)("d")3b-3=<=12color(white)("dddd")=>color(white)("dddd")b<=(12+3)/3`

`color(white)("ddddddddddddddddddd")=>color(white)("dddd")b<=+5`

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`-3<=b<=5`