Solving inequalities. And "real numbers."

26 + 6b /= 2(3b+4)
26 + 6b /= 6b +8
6b /= 6b -18
b /= -18

In the uploaded imagine the solutions don't match mine.

Question

Solving inequalities. And "real numbers."

26 + 6b  >/= 2(3b+4)
26 + 6b >/= 6b +8
6b >/= 6b -18
b >/= -18

In the uploaded imagine the solutions don't match mine.

anonymous · Answer

attachment

anonymous · Answer

How can $6b$ can be greater than or equal to $6b-18$ ??

igreen · Answer

$26 + 6b \ge 2(3b + 4)$

First distribute 2 into the parenthesis:

$26 + 6b \ge 6b + 8$

Subtract 26 to both sides:

$6b \ge 6b - 18$

Subtract 6b to both sides:

What's 6b - 6b? @ShhhhhIDK

anonymous · Answer

@iGreen 0...?

igreen · Answer

Yes.. that removes the variables..which means we cannot solve..

igreen · Answer

So what do you think the answer is? @ShhhhhIDK

anonymous · Answer

but then how is the answer "all real numbers" @iGreen. Did my school get it wrong?

igreen · Answer

It isn't.

perl · Answer

you have a true statement, so the answer is all real numbers

igreen · Answer

You removed the variable..you cannot solve anymore..

perl · Answer

26 + 6b >= 2(3b+4)

26 + 6b >= 6b + 8

subtract 6b from both sides

26 >= 8  , this is true . so the answer is all real numbers satisfy this inequality

anonymous · Answer

No Solution??

anonymous · Answer

@perl and @iGreen the two of you have given me different answers lol and now I'm even more confused. I thought it was no solution.

igreen · Answer

It is no solution.

anonymous · Answer

@perl they didn't teach me to to solve the inequalities like that is there a rule I'm missing?

igreen · Answer

Wait..I'm confused.

anonymous · Answer

Wait, we should have some time to think it properly..

anonymous · Answer

@iGreen I said that on the test but it was the wrong answer the right answer was all real numbers but I''m not completely sure how that's why I'm asking perl to clarify.

perl · Answer

solution is a) all real numbers

anonymous · Answer

If the answer is all real numbers, then for every number you choose, that should satisfy the inequality.. :)

igreen · Answer

Perl is correct..it's all real numbers.

anonymous · Answer

Yep..

anonymous · Answer

@waterineyes  Thank you.

perl · Answer

shhh, try to think of it backwards. 

suppose you start with  

b = b  ,  true for any real number

now 

6b = 6b   , also true for any real number

now 

26 > 8   , so 

26 + 6b > 8 + 6b

anonymous · Answer

$6b$ is always greater than the same quantity $-$ 18..

anonymous · Answer

Oh my gosh I'm an idiot! @perl  thank you!

anonymous · Answer

That makes so much sense. I'm an idiot lol.

perl · Answer

its a fair question :)

anonymous · Answer

I am too... :P

anonymous · Answer

For equal too case, answer is no solution.. @iGreen

anonymous · Answer

*equal to..