2 years ago

Twice the difference of a number and 9 is at least 17.

Mathematics

1 answer:

victus00 [196]2 years ago

8 0

Answer:

x ≥ 12.5

Step-by-step explanation:

2(x-9) ≥ 17---Use Distributive Property

2x-18 ≥ 17

2x-18+18 ≥ 17+18

2x ≥ 25

2x/2 ≥ 25/2

x ≥ 12.5

I hope this helps!

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Solution:

The rationalisation factor for $\frac{1}{ a - \sqrt{b} }$ is $a + \sqrt{b}$

So, let us apply it here.

$\frac{1}{5 - \sqrt{2} }$

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

$= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}$