Graph -8 ≥-5x + 2 > -38

I really need help!!!

Question 5

Which of the following is the correct graph of the solution to the inequality -8 greater than or equal to -5x + 2 > -38?
Answer

number line with a closed dot on 2 and an open dot on 8 and shading in between.

number line with an open dot at 2 with shading to the left and another open dot at 8 with shading to the right.

number line with closed dots at 2 and 8 with shading between the 2 and the 8.

number line with an open dot at 8 and at 2 with shading in between.



Question 6


Which of the following is the correct graph of the compound inequality 4p + 1 > -11 or 6p + 3 < 39?
Answer

number line with shading everywhere.

a number line with closed circles at -3 and 6 and shading in between.

number line with open dots at ¨C3 and 6 and shading to the right of 6 and to the left of ¨C3.

number line with open dot at ¨C2 and at 5 with shading in between.



Question 7


Which of the following is the correct graph of the compound inequality n > 5 and n < 3?
Answer

number line with open dots at 3 and 5 and shading to the left of the 3 and to the right of the 5.

number line with open dots at 3 and 5 and shading between them.

open number line to illustrate the ¡°no real solutions¡± answer to this inequality problem.

number line with open dots at ¨C3 and ¨C5 and shading between them.
17:50 Fri 16th Dec 2011
 
Avatar Image
jake-the-peg
Best Answer
The best way to approach these questions with inequalities is to start by drawing the line as if it was an equals.

So for -5x + 2 > -38 draw -5x + 2 = -38 which of course is -5x=-40 (when you take 2 away from both sides ) and x=8 (when you divide both sides by -5)

so you draw a verticle line x=8 and go back to the inequality x>8 this is an easy one you'll imediately...
18:06 Fri 16th Dec 2011 Go To Best Answer

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Have you tried drawing/sketching them on graph paper?
Graph -8 ≥-5x + 2 > -38
We have two rules: -5x + 2 > -38 and -5x + 2 <= -8
Simplify: x<8 and x>=2
So x = 2 or more but is less than 8. So I think that is your answer A- number line with a closed dot on 2 and an open dot on 8 and shading in between.
Now try the others
Q7 is the easiest of these.
Just draw a number line, and mark on 3 and 5. You are interested in the points to the left of (less than) 3 and to the right of (greater than) 5.
Make sure you know the difference between an open circle and a closed circle.

Then you will have your answer
The best way to approach these questions with inequalities is to start by drawing the line as if it was an equals.

So for -5x + 2 > -38 draw -5x + 2 = -38 which of course is -5x=-40 (when you take 2 away from both sides ) and x=8 (when you divide both sides by -5)

so you draw a verticle line x=8 and go back to the inequality x>8 this is an easy one you'll imediately know which side to shade but if it was more difficult just pick a point and say is this true or not

Lets say the point (1,1) is x>8? no - so this is not the side where it's true

Now lets look at questions where there is an "or" or an "and"


We do the same thing with both lines and we get two shade areas

if the question is an or then both shaded areas will be valid answers - if it's an and then the correct ares is only the area where the two shadings overlap.

Whatch out for the greater or equal sign or the less or equal to in those cases the line itself is part of the answer.

Draw them out on square paper and compare to the multple choice - with practice you may be able to work it out without doing the drawing but that will take practice.

I think you may be having difficulty because you haven't yet put in enough practice and are trying to do it in your head straight off

so we now have two shaded areas
Take care when solving inequalities where there is a negative sign in front of the x
e.g. -5x + 2 > -38
Do it in steps if you are unsure.
Subtract two from both sides of the inequality:
-5x>-40
So 5x<40. Note that the inequality sign has changed round. Try some different values for x to see if you can work out why this is the case
If the idea of plotting graphs seem laborious a quicker method is to use WolframAlpha. Just put the equation next to the word 'plot'

http://www.wolframalp...input/?i=plot+2x%2B2+

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