Problem Solving

Im having a hard time figuring this really simple question

Solve the following inequality for x:
2x>x+10>-x

the ans is [spoiler]x>10[/spoiler]

Nidhs wrote:Im having a hard time figuring this really simple question

Solve the following inequality for x:
2x>x+10>-x

We treat multiple part inequalities the same as regular inequalities: whatever we do to 1 piece we have to do to the entire thing.

Here, we can subtract x from all 3 parts to get:

x > 10 > -2x

and that's really the best we can do.

So, while it's true that x > 10, that's not the ENTIRE answer to the question. If we just focus on the right side, we get:

10 > -2x

-5 < x

So, we have two rules:

x > 10 and x > -5. Since they're both ">", we take the more extreme limintation and end up simply with:

x > 10.

Thank you. So when do we need to test if an inequality is correct by substituting in the question stem?