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Solve (2x+3)/(x^(2)+x-12) lt (1)/(2)....

Solve `(2x+3)/(x^(2)+x-12) lt (1)/(2)`.

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The correct Answer is:
`x in (-oo,-4) uu (-3,3) uu (6,oo)`
`(2x+3)/(x^(2)+x-12) lt (1)/(2)`
`implies (2x+3)/(x^(2)-x-12)-(1)/(2) lt 0`
`implies (4x+6-x^(2)-x+12)/(x^(2)+x-12)`
`implies (x^(2)-3x-18)/((x+4)(x-3)) gt 0`
`implies ((x-6)(x+3))/((x+4)(x-3)) gt 0`

`x in (-oo,-4)uu(-3,3)uu(6,oo)`
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CENGAGE-INEQUALITIES AND MODULUS-Single correct Answer
  1. Solve (2x+3)/(x^(2)+x-12) lt (1)/(2).

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  2. If f(x)=ax^(2)+bx+c and f(-1) ge -4, f(1) le 0 and f(3) ge 5, then the...

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  3. The complete set of values of x for which (x^(3)(x-1)^(2)(x+4))/((x+...

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  4. The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x...

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  5. The solution set of inequality ((e^(x)-1)(2x-3)(x^(2)+x+2))/((sinx-...

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  6. The solution set of inequality (1)/(2^(x)-1) gt (1)/(1-2^(x-1)) is

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  7. Let A={x:x^(2)-4x+3 lt 0,x in R } B={x: 2^(1-x)+p le 0 , x^(2)-2(p+7)...

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  8. Let a, b gt 0 satisfies a^(3)+b^(3)=a-b. Then

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  9. The number of integers satisfying |2x-3|+|x+5| le |x-8| is

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  10. Which of the following is not the solution of |2x+5|-|x-3| ge |x+8| ...

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  11. The number of integral values of x satisfying the equation |x-|x-4||=4...

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  12. The solution of |2x-3| lt |x+2| is

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  13. The solution set of the inequation |(1)/(x)-2| lt 4, is

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  14. The solution of |x+(1)/(x)| gt 2 is

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  15. The solution of the inequality (|x+2|-|x|)/(sqrt(8-x^(3))) ge 0 is

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  16. If |(12x)/(4x^(2)+9)| le 1, then

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  17. Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then t...

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  18. The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+...

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  19. If |x^2- 2x- 8| + |x^2+ x -2|= 3|x +2|, then the set of all real valu...

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  20. The number of integers satisfying the equation |x|+|(4-x^(2))/(x)|=|(4...

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  21. The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses

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