If -5- p -2 and 7- q -9- then what is the range of p - q - A- -2-7B- 2-7C- 7-2D- -7-2

The correct option is B (2, 7) 5 lt; p lt; 2 and 7 lt;q lt;9 Adding two inequalities with same natured inequalities will preserve the sign. So addi ...

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Standard XII

Mathematics

Properties of inequalities

If -5< p <-2 ...

Question

If $- 5 < p < - 2$ and $7 < q < 9$ , then what is the range of p + q?

(-2, -7)

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(2, 7)

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(7, 2)

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(-7, -2)

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Solution

The correct option is B (2, 7)
$- 5 < p < - 2$ and $7 < q < 9$
Adding two inequalities with same natured inequalities will preserve the sign.
So adding the two inequalities:
$- 5 + 7 < p + q < - 2 + 9$
$\Rightarrow 2 < p + q < 7$

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If −5<p<−2 and 7<q<9, then what is the range of p + q?

The correct option is B (2, 7)−5<p<−2 and 7<q<9 Adding two inequalities with same natured inequalities will preserve the sign. So adding the two inequalities: −5+7<p+q<−2+9 ⇒2<p+q<7

If $- 5 < p < - 2$ and $7 < q < 9$ , then what is the range of p + q?

The correct option is B (2, 7)
$- 5 < p < - 2$ and $7 < q < 9$
Adding two inequalities with same natured inequalities will preserve the sign.
So adding the two inequalities:
$- 5 + 7 < p + q < - 2 + 9$
$\Rightarrow 2 < p + q < 7$