Which of the following is a solution set to the equation: x(x-1)(x-6)

Question

Which of the following is a solution set to the equation:  x(x-1)(x-6)<0  ?

A.  1<x ≤ 6

B.  x ≤ 0

C.  x < 0

D.  6 ≤ x

E.  0 ≤ x

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szcz · Answer

x(x−1)(x−6)<0
If the above equation is equated to 0, the roots will be x=0, x=1, x=6
Hence on plotting we find that the above equation will be negative at these ranges.

X<0 and 1<x<6

Answer Option C.

hinasingh · Answer

Which of the following is a solution set to the equation: x(x−1)(x−6)<0

A. 1<x≤6
not true for x =6.
B. x≤0
not true for x =0
C. x<0
True for all values of x
D. 6≤x
not true for any values of x>=6
E. 0≤x
not true for x = 0,1,6 or for 0<x<1
Answer C

Shane04 · Answer

Which of the following is a solution set to the equation:  x(x-1)(x-6)<0  ?

A.  1<x ≤ 6

B.  x ≤ 0

C.  x < 0

D.  6 ≤ x

E.  0 ≤ x

Bunuel  can you explain the solution to getting C?

Bunuel · Answer

x(x-1)(x-6)<0 Here is how to solve the above inequality easily. The "roots", in ascending order, are 0, 1, and 6, which gives us 4 ranges: x < 0 ; 0 < x < 1 ; 1 < x < 6 ; x > 6 . Next, test an extreme value for x : if x is some large enough number, say 10, then all three multiples will be positive, giving a positive result for the whole expression. So when x > 6 , the expression is positive. Now the trick: as in the 4th range, the expression is positive, then in the 3rd it'll be negative, in the 2nd it'll be positive, and finally in the 1st, it'll be negative: ext{(- + - +)} . So, the ranges when the expression is negative are: x < 0 and 1 < x < 6 . P.S. You can apply this technique to any inequality of the form (ax - b)(cx - d)(ex - f)... > 0 or < 0 . If one of the factors is in the form (b - ax) instead of (ax - b) , simply rewrite it as -(ax - b) and adjust the inequality sign accordingly. For example, consider the inequality (4 - x)(2 + x) > 0 . Rewrite it as -(x - 4)(2 + x) > 0 . Multiply by -1 and flip the sign: (x - 4)(2 + x) < 0 . The "roots", in ascending order, are -2 and 4, giving us three ranges: x < -2 , -2 < x < 4 , and x > 4 . If x is some large enough number, say 100, both factors will be positive, yielding a positive result for the entire expression. Thus, when x > 4 , the expression is positive. Now, apply the alternating sign trick: as the expression is positive in the 3rd range, it will be negative in the 2nd range, and positive in the 1st range: ext{(+ - +)} . Therefore, the ranges where the expression is negative are: -2 < x < 4 . Check the links below: 9. Inequalities Theory Inequalities Made Easy! Inequalities: Tips and hints Arithmetic with Inequalities Wavy Line Method Application - Complex Algebraic Inequalities Solving Quadratic Inequalities: Graphic Approach Inequalities - Quadratic Inequalities Graphic approach to problems with inequalities Inequalities trick INEQUATIONS(Inequalities) Part 1 INEQUATIONS(Inequalities) Part 2 Questions Inequality and absolute value questions from my collection DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread

bumpbot · Answer

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Which of the following is a solution set to the equation: x(x-1)(x-6)<

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