1.

Which of the following is the solution set of |(2)/(3)u-5|gt 8 ?

Answer»

`{u: -(39)/(2)LT u lt (9)/(2)}`
`{u : -(9)/(2) lt u lt (39)/(2)}`
`{u : u gt (39)/(2)` or `u lt -(9)/(2)}`
`{u : u gt (9)/(2)` or `u lt -(39)/(2)}`

Solution :What does it MEAN if `|(2)/(3)u-5|gt 8` ? It means if the expression between the ABSOLUTE value bars is positive, it's greater than `+8` or, if the expression between the bars is negative, it's less than `-8`. In other words, `(2)/(3)u-5` is outside the range of `-8` to `+8` :
`{:((2)/(3)u-5 gt8" "),(""(2)/(3)u gt 13),(""u gt (39)/(2)):} {:(" "(2)/(3)u-5 lt -8),(""(2)/(3)u lt - 3),(""u lt - (9)/(2)):}`
In fact, there's a general rule that applies here : To solve an inequality in the form |Whatever| lt p, where `p gt 0` , just put that ''Whatever'' inside the range `-p` to p:
|Whatever| lt p means -plt whateverltp
For example, `|x-5|lt 14` becomes `-14 lt x - 5 lt 14`.


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