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What is the solution: #6(n -2)>5n+ 5#?

Answer 1

Eva Adamson

#n>17#

#color(blue)(6(n-2)>5n+5#

We can solve this inequality by isolating #n# as much as possible

We do the same operation on both sides to achieve this

#rarrcolor(red)(6(n-2))>5n+5#

Use the distributive property to expand #6(n-2)#

#color(brown)(a(b+c)=ab+ac#

#rarrcolor(red)(6(n)-6(2))>5n+5#

#rarr6n-12>5n+5#

Add #12# both sides

#rarr6n-12+color(red)(12)>5n+5+color(red)(12)#

#rarr6n>5n+17#

Subtract #5n# both sides

#rarr6n-color(red)(5n)>5n+17-color(red)(5n)#

#color(green)(rArrn>17#

Hopefully this helps!

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Answer 2

Avery Alexander

To solve the inequality (6(n - 2) > 5n + 5), follow these steps:

Distribute the 6 on the left side: [6n - 12 > 5n + 5]
Subtract (5n) from both sides: [6n - 5n - 12 > 5n - 5n + 5] [n - 12 > 5]
Add 12 to both sides: [n - 12 + 12 > 5 + 12] [n > 17]

So, the solution to the inequality is (n > 17).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What is the solution: #6(n -2)&gt;5n+ 5#?

What is the solution: #6(n -2)>5n+ 5#?