Which of the following inequalities have at least two soluti
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13 Apr 2023, 00:43
This question can be solved by understanding number properties for the numbers between -1 and 1.
A. For the infinity of numbers greater than 0 and up to 1,
(3/7)x < x will be true so at least two solutions satisfy this condition. This is because a positive fraction of a positive number will always be less than the positive number.
B. For the infinity of numbers greater than -1 and less than 0,
x < x^2 will be true so at least two solutions satisfy this condition. This is because numbers greater than -1 and less than zero (negative proper fractions) are get larger as the power is raised but not as large as zero.
C. For the all real numbers including all the numbers between than zero -1 and 1, subtracting a positive number from it will make it smaller and adding a positive number will make it larger.
So the left hand side of the inequality x - 1/2 < x + 2/3 will always be less than the right hand side of the inequality, hence it satisfies the condition that there are at least two solutions to the inequality as well.