23-7x-3x(greater than or equal to sign)-11 Please Help
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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?
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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?
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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
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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):
\[23>1\]
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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
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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
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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?
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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?
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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?
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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
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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 :)