anonymous
  • anonymous
1. x – 3 > –9 2. –2x + 1 ≤ –11 3. 10 < –3x + 1 4. 2(x + 5) > 8x – 8 5. –2(x – 3) ≥ 5 – (x + 3) Solve each and graph for each
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
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anonymous
  • anonymous
@AbdullahM
anonymous
  • anonymous
1. x> -6
AbdullahM
  • AbdullahM
correct :)

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More answers

anonymous
  • anonymous
how would i graph this
AbdullahM
  • AbdullahM
|dw:1435336629065:dw|
AbdullahM
  • AbdullahM
You could use: https://www.desmos.com/calculator
anonymous
  • anonymous
i mean on a number line sorry
anonymous
  • anonymous
it would be an open circle?
AbdullahM
  • AbdullahM
yes
anonymous
  • anonymous
Do you have a website for the number line?
AbdullahM
  • AbdullahM
essentially, you can use the website and only look at the x-axis
AbdullahM
  • AbdullahM
and since you see the graph has a dashed line, that means an open circle. When the line on the graph is solid, then that means a closed circle.
anonymous
  • anonymous
ok so closed
AbdullahM
  • AbdullahM
|dw:1435336897914:dw| this has a dashed line so it means open circle
AbdullahM
  • AbdullahM
I drew an orange box around the dashed line.
anonymous
  • anonymous
alright i can graph the rest i just need help solving the rest
anonymous
  • anonymous
-2x +1 < -11 \[-2x +1 \le -11\]
AbdullahM
  • AbdullahM
for graphing it on a number line: |dw:1435337002162:dw|
AbdullahM
  • AbdullahM
For #2, we would first take the +1 to the other side. So we have to subtract that on both sides.
anonymous
  • anonymous
so -12
anonymous
  • anonymous
-2x less than or equal to -12
AbdullahM
  • AbdullahM
now we have \(\sf -2x\le -12\)
anonymous
  • anonymous
now devide -2?
anonymous
  • anonymous
divide*
AbdullahM
  • AbdullahM
Do you know that when you divide by a negative number on both sides that the sign flips
anonymous
  • anonymous
so it goes to >?
anonymous
  • anonymous
or this
AbdullahM
  • AbdullahM
For example: \(\sf\Large -x \le 5\) then \(\sf\Large x \ge 5\) another example: \(\sf\Large -2y > 6\) then \(\sf\Large y<-3\)
anonymous
  • anonymous
does it ever switch from \[\le \to \]
anonymous
  • anonymous
not showign up
anonymous
  • anonymous
without the line under it
AbdullahM
  • AbdullahM
no it can't
anonymous
  • anonymous
but this answer is x=6
AbdullahM
  • AbdullahM
\(\color{blue}{\text{Originally Posted by}}\) @AbdullahM now we have \(\sf -2x\le -12\) \(\color{blue}{\text{End of Quote}}\) if we divide -2, and also we have to change the sign, what do we get?
anonymous
  • anonymous
x= 6
anonymous
  • anonymous
oh x > 6
AbdullahM
  • AbdullahM
no, it would be \(\sf\Large x\ge6\)
anonymous
  • anonymous
yeah thats i meant my b
anonymous
  • anonymous
could i also say greater than or equal to?
AbdullahM
  • AbdullahM
remember these are the opposites: \(\sf \le\) and \(\sf \ge\) are opposites < and > are opposites
anonymous
  • anonymous
and this circle would be open?
AbdullahM
  • AbdullahM
nope closed
AbdullahM
  • AbdullahM
http://prntscr.com/7ln08a from: http://www.studyzone.org/mtestprep/math8/a/graphing_inequalities7l.cfm
anonymous
  • anonymous
|dw:1435337698545:dw|
anonymous
  • anonymous
@AbdullahM
AbdullahM
  • AbdullahM
correct :)
anonymous
  • anonymous
10 < -3x + 1
anonymous
  • anonymous
-1 both sides
anonymous
  • anonymous
9 < -3x
AbdullahM
  • AbdullahM
10 < –3x + 1 lets make our life easier and not have to do the switching signs. So lets take 3x to the other side by addition
anonymous
  • anonymous
oh alright
anonymous
  • anonymous
+3x both sides 3x + 10 < 1 3x < -9 x< -3
anonymous
  • anonymous
|dw:1435338193021:dw|
anonymous
  • anonymous
@AbdullahM
anonymous
  • anonymous
i might have made a mistake
anonymous
  • anonymous
Should i have flipped the sign?
AbdullahM
  • AbdullahM
splendid work, you made no mistakes :)
AbdullahM
  • AbdullahM
we only flip the sign when we divide by a negative number
anonymous
  • anonymous
oh alright
AbdullahM
  • AbdullahM
2(x + 5) > 8x – 8
anonymous
  • anonymous
2(x + 5) > 8x - 8
AbdullahM
  • AbdullahM
First we have to take care of 2(x+5) distribute the 2 inside
anonymous
  • anonymous
2x + 10 > 8x - 8
anonymous
  • anonymous
-8x both sides -6x + 10 > -8 -10 both sides -6x> -18 divide -6 both sides x < 3
anonymous
  • anonymous
|dw:1435338649893:dw|
AbdullahM
  • AbdullahM
wow, amazing work once again! :D
anonymous
  • anonymous
Thank you :)
anonymous
  • anonymous
-2(x - 3) > 5 - (x +3)
AbdullahM
  • AbdullahM
–2(x – 3) ≥ 5 – (x + 3) this time we have both sides where we have to dsitribute. Be careful, they have a negative number outside that needs to be distributed
anonymous
  • anonymous
-2x + 6 > 5 -x - 3 @AbdullahM ?
AbdullahM
  • AbdullahM
amazing work! :D
AbdullahM
  • AbdullahM
no we can add the 2x to both sides and work from there :)
anonymous
  • anonymous
why te 2x?
anonymous
  • anonymous
+x both sides -x + 6 > 5-3 -6 both sides -x > -4 divide by -1 x < 4
AbdullahM
  • AbdullahM
so we don't have to divide by a negative number on both sides, but it seems like you have mastered that trick anyways :D
AbdullahM
  • AbdullahM
not really a rtick, more like a rule xD
anonymous
  • anonymous
yeah :p i thought it' be easier
AbdullahM
  • AbdullahM
great work again :)
anonymous
  • anonymous
|dw:1435339061662:dw|
anonymous
  • anonymous
@AbdullahM
anonymous
  • anonymous
Explain, in complete sentences, when you would use an open circle or a closed circle, and when you would shade to the right or left, to graph an inequality on the number line. (3 points) 7. Describe a real life scenario where inequalities are used and state the inequality. (2 points)
AbdullahM
  • AbdullahM
\(\color{blue}{\text{Originally Posted by}}\) @AbdullahM http://prntscr.com/7ln08a from: http://www.studyzone.org/mtestprep/math8/a/graphing_inequalities7l.cfm \(\color{blue}{\text{End of Quote}}\) use this for the first question
anonymous
  • anonymous
alright and i think i did my last graph wrong
anonymous
  • anonymous
|dw:1435339286981:dw|
AbdullahM
  • AbdullahM
open circle, not closed. and everything else is correct
AbdullahM
  • AbdullahM
anonymous
  • anonymous
@AbdullahM Thank you for the help! You are a great teacher :)
AbdullahM
  • AbdullahM
anytime, that's why I'm on OpenStudy to help.
anonymous
  • anonymous
That's all i need for today but i'll hit ya up if i need help another time, Have a good afternoon!
AbdullahM
  • AbdullahM
sure :)

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