# Given #-2x-5 < -2# I got #-2x < 3#. Is this correct? How do I solve from here?

Your answer is not wrong; but it is incomplete.

I see two approaches to this:

Method 1: Keep in mind the inequality sign reversal rule, which allows you to multiply or divide both sides of an inequality by any negative number.

Method 2: Keep in mind that you can multiply or divide both sides of an inequality by any number larger than zero, or you can add or subtract the same amount from each side without changing the inequality's orientation.

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As a general rule, it's important to keep in mind that if you multiply any of an inequality's sides by a negative number, you must reverse the inequality sign's direction because each side's sign has changed, essentially reflecting the relationship's original origin on the number line.

Next, some algebra

And split each side in half:

It takes a little longer to solve if you simply add or subtract the appropriate amounts from each side of the inequality, but here it is.

-5 color(blue)(+ 5) #-2x color(red)(+ 2x) color(blue)(+ 5)

Change the sequence:

And split each side in half:

The most crucial part is probably this one: You can always double-check your solution by solving the equality first, adding values to either side of the point where you believe the inequality to emerge, or simply drawing or plotting it.

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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.

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.

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.

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