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Mathematics 19 Online
OpenStudy (anonymous):

23-7x-3x(greater than or equal to sign)-11 Please Help

OpenStudy (lgbasallote):

\[\huge 23 - 7x - 3x \ge -11?\] this sunds fishy

OpenStudy (lgbasallote):

sounds*

OpenStudy (anonymous):

lol really?

OpenStudy (anonymous):

can you help?

OpenStudy (lgbasallote):

so is that the question?

OpenStudy (anonymous):

yeah thats the question

OpenStudy (lgbasallote):

first combine - 7x and -3x what do you get?

OpenStudy (anonymous):

am i adding?

OpenStudy (lgbasallote):

depends what you mean...

OpenStudy (anonymous):

like with the -7x and -3x so am i subtracting? or adding?

OpenStudy (lgbasallote):

like i said...depends what you mean...we can only know if what you're thinking is right or wrong if you tell me what you get for -7x -3x

OpenStudy (anonymous):

-10

OpenStudy (lgbasallote):

and the x?

OpenStudy (anonymous):

-10x?

OpenStudy (lgbasallote):

yes

OpenStudy (anonymous):

right ....

OpenStudy (lgbasallote):

so the equation becomes \[\implies 23 - 10x \ge -11\] now add 10x to both sides

OpenStudy (anonymous):

okay im doing it now

OpenStudy (anonymous):

-1

OpenStudy (anonymous):

\[23>1\]

OpenStudy (anonymous):

messed up on the sign

OpenStudy (lgbasallote):

i have no idea what you just did.... o.O

OpenStudy (lgbasallote):

well actually i do

OpenStudy (anonymous):

lol me either

OpenStudy (lgbasallote):

1) i said add -10x to BOTH sides..not just the left side 2) you cant combine -11 and -10 x 3) even if you can combine -11 and -10x it should be -21 not 1

OpenStudy (lgbasallote):

oh wait...my number 2 and 3 are wrong

OpenStudy (lgbasallote):

2) you cant combine -11 and 10x 3) even if you can combine -11 and 10x it should be -1 not 1

OpenStudy (anonymous):

yeah i caught that

OpenStudy (anonymous):

soo whats next after that? Because now i have 23-1

OpenStudy (lgbasallote):

no you dont

OpenStudy (anonymous):

ughhh im so confused so what do i have

OpenStudy (lgbasallote):

let's start from the top \[23 - 10x \ge -11\] add 10x to both sides. what do you get?

OpenStudy (lgbasallote):

remember those three things i said

OpenStudy (anonymous):

right and i get -1

OpenStudy (lgbasallote):

let me give a demonstration... \[1 - 2x \ge 3\] if i add 2x to both sides i get \[\implies 1 - 2x + 2x \ge 3 + 2x\] now combine like terms \[\implies 1 \ge 3 + 2x\] now subtract 3 from both sides \[\implies 1 -3 \ge 3 + 2x - 3\] combine like terms \[\implies -2 \ge 2x\] divide both sides by 2 \[\implies -1 \ge x\] or simply \(x \le -1\) got it now?

OpenStudy (anonymous):

its not really the same thing because that one is simple an dthis on eis not so i cant really relate t that example

OpenStudy (lgbasallote):

oh it's very similar i assure you... because i added 2x here...same way as i am instructing you to add 10x there

OpenStudy (anonymous):

and i did

OpenStudy (lgbasallote):

you keep combining -11 and 10x...but you see i didnt combine 3 and 2x

OpenStudy (anonymous):

so add 10x to the 23?

OpenStudy (lgbasallote):

did i combine 2x to 1?

OpenStudy (anonymous):

no..

OpenStudy (lgbasallote):

exactly

OpenStudy (anonymous):

okay then idk

OpenStudy (lgbasallote):

here's another one \[30 - 24x \ge -15\] add 24x to both sides \[30 - 24x + 24x \ge -15 + 24x\] combine \[30 \ge -15 + 24x\] add 15 to both sides \[30 + 15 \ge -15 + 24x + 15\] combine like terms \[45 \ge 24x\] divide both sides by 24 \[\frac{45}{24} \ge x\] is that still simple?

OpenStudy (lgbasallote):

and btw..just so you know...i used the exact same scenario as the question \[23 - 10x \ge -11\] and \[30 - 24x \ge -15\] see the similarity?

OpenStudy (anonymous):

okay yeah.. then its [23>-11+10x\]

OpenStudy (anonymous):

without the {}

OpenStudy (lgbasallote):

right

OpenStudy (lgbasallote):

now add 11 to both sides

OpenStudy (anonymous):

final answer 34 over 10 >x

OpenStudy (lgbasallote):

hmm close... \[\frac{34}{10} \ge x\]

OpenStudy (anonymous):

yeah like thAT..

OpenStudy (anonymous):

Whew!!! That took forever but thank you for not giving up on me :)

OpenStudy (lgbasallote):

haha i never do :DD

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