Question

can someone help me here? it's asking to explain in words where the mistake in the solution of the inequality is.

Answer 1

Answer and Step-by-step explanation:

The mistake is that the sign (<) isn't flipped.

When a negative number is multiplied, the sign of the inequality flips to go the other way, so < would go >.

Answer 2

The mistake occurs in the second to last line. When you divide both sides by a negative number, the inequality sign should flip.

So the answer should be x > -5 instead of x < -5.

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Here's why the inequality sign flips

Let's start with the inequality -2x < 10. Add 2x to both sides and we get 0 < 10+2x which is the same as 0 < 2x+10

Then subtract 10 from both sides to end up with -10 < 2x

We can flip both sides of -10 < 2x to end up with 2x > -10. Note the inequality sign flips, as well as the left and right sides.

Afterward, we solve 2x > -10 by dividing both sides by 2 to get x > -5. The inequality sign does not flip when we divide both sides by a positive number.