Algebra

Algebra Level pending

∣ 5 − 2 3 x ∣ < 1 \left|5-\frac 2{3x} \right|<1

Solve the inequality above.

1 9 < x < 1 6 \frac 19 < x < \frac 16 1 9 > x or x < 1 6 \frac 19 > x \text{ or } x< \frac 16 x > 1 9 x>\frac 19 x > 0 x>0

Edward Adan by Edward Adan , 26, Bangladesh

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1 solution

Edward Adan
Jun 26, 2016

∣ 5 − 2 ( 3 x ) ∣ < 1 |5-2(3x)|<1

-1<5-2/(3x)<1; 5-2/(3x)<1, >>2/(3x)+1>5, >>2/(3x)>4, >>3x/2<1/4, >>x<1/6

again,5-2/(3x)>-1, >>2/(3x)<6, >>1/x<9, >>x>1/9

then the result is 1 / 9 < x < 1 / 6 1/9<x<1/6

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