Why did my teacher mark this wrong? (Inequality problem)

[Ladybug]

I'm looking over my tests, getting ready for math finals...and on one of my easier (beginning algebra, inequalities, linear equations) tests I came across this problem I couldn't understand. I'm sure it's probably really easy, and I just don't see it or something! But I can't figure it out. Here it is:

2x+7<2(x+10)

So I marked it as no solution, with {}, because it simplifies to 2x+7<2x+20 which cancels out the x's. (Subtract 2x from both sides, right?) That leaves no x to graph or solve for. Why did I get this wrong?

Thanks for any help. I appreciate it!

 

[royhaas]

The inequality is true for all values of x.

 

[Deleted member 4993]

2x+7<2(x+10) So I marked it as no solution, with {}, because it simplifies to 2x+7<2x+20 which cancels out the x's. (Subtract 2x from both sides, right?) That leaves no x to graph or solve for. Why did I get this wrong?

Your "steps" are correct - however interpretation is wrong.

When you finish you get

7 < 20 --- which is always true.

That means the above inequality is always true - for any value of 'x' - minus infinity to plus infinity.

So actually you have infinite number of solutions (as opposed to zero - or 'no' - solution)

 

[Ladybug]

Thanks a lot! So it would have been all real numbers, or {R}? I didn't even see that. Again, it's the small stuff (basic arithmetic!) in math that gets the better of me.