Let us learn about Inequalities.
First of all let us understand what is Inequalities ?
A number a is greater than a number b if a−b is positive. In symbols
this is written as a > b.
Thus 2 > 1 because 2 − 1 = 1 is positive,
3 > −1 because 3 − (−1) = 4 is positive,
BUT −1 > 2 is false because −1 − 2 = −3 is negative.
Example 1 Prove or disprove the following inequalities.
(a)
(b)
Solution :
(a) As a decimal, 1/4 = 0.25 and so 0.4 − 1/4 = 0.4 − 0.25 = 0.15,
which is positive. Thus 0.4 > 1/4 is true.
(b) Here (0.7)2 = 0.7 × 0.7 = 0.49. As a fraction 1/2 is 0.5. In this
case, (0.7)2−1/2 = 0.49−0.5 = −0.01, which is negative. This means
that the inequality (0.7)2 > 1/2 is false.
Hope the above explanation helped you, now let me give you more examples.
First of all let us understand what is Inequalities ?
A number a is greater than a number b if a−b is positive. In symbols
this is written as a > b.
Thus 2 > 1 because 2 − 1 = 1 is positive,
3 > −1 because 3 − (−1) = 4 is positive,
BUT −1 > 2 is false because −1 − 2 = −3 is negative.
Example 1 Prove or disprove the following inequalities.
(a)
(b)
Solution :
(a) As a decimal, 1/4 = 0.25 and so 0.4 − 1/4 = 0.4 − 0.25 = 0.15,
which is positive. Thus 0.4 > 1/4 is true.
(b) Here (0.7)2 = 0.7 × 0.7 = 0.49. As a fraction 1/2 is 0.5. In this
case, (0.7)2−1/2 = 0.49−0.5 = −0.01, which is negative. This means
that the inequality (0.7)2 > 1/2 is false.
Hope the above explanation helped you, now let me give you more examples.
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