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How do you solve and write the following in interval notation: #-7x-2< -8x-6#?

Answer 1

Hazel Anglin

#(-oo, -4)#

Given: #-7x-2 < -8x - 6#

Add #8x# to both sides of the inequality:

#-7x-2 + 8x < cancel(-8x) - 6 + cancel(8x)#

Simplify:

#x - 2 < -6#

Add #2@ to both sides of the inequality:

#x - 2 + 2 < -6 + 2#

Simplify:

#x < -4#

Interval notation: #(-oo, -4)#

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Answer 2

Eva Adamson

To solve the inequality -7x - 2 < -8x - 6 and write it in interval notation:

Add 8x to both sides: x - 2 < -6
Add 2 to both sides: x < -4

So, the solution to the inequality is x < -4.

In interval notation, this is written as: (-∞, -4).

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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.

How do you solve and write the following in interval notation: #-7x-2&lt; -8x-6#?

How do you solve and write the following in interval notation: #-7x-2< -8x-6#?