# Inequalities HELP!!

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• Aug 25th 2012, 03:05 PM
zales127
Inequalities HELP!!
Need Help!!! This is not for a graded quiz. Im trying to tutor my son but Im no math wiz myself and need to figure out the correct answers so that I know when I try to help him!!!

Question 1
Which of the following is equivalent to |4x + 5| = 88?
-4x + 5 = 88
4x + 5 = -88
4x + 5 = 88
4x + 5 = 88 or 4x + 5 = -88

Question 2
Solve |6x – 5| = 25.
{5, -5}
{5, -10/3}
{-25, 25}
{10/3, -5}

Question 3
Which statement has the solution shown on the number line?

|x + 1| = 4
|x – 1| = 4
|x| = 3
none of the above

Question 4
Which statement is equivalent to |3x + 7| ≤ 30?
3x + 7 ≤ 30 or 3x + 7 ≥ -30
-30 ≤ 3x + 7 ≤ 30
3x + 7 ≤ 30
3x = 7 ≤ -30

Question 5
Solve |x+5| < 9.
{x| x < 4 or x > -14}
{x| x < 4 or x > -4}
{x| -14 < x < 4}
{x| -4 < x < 4}

Question 6
Which inequality has the solution shown on the number line?

|4 – x| ≤1
|x – 4| ≤ 1
|x + 2| ≥ 5
|x + 2| ≥ 7

Question 7
Which statement is equivalent to |x + 9| > 15?
x + 9 > 15
x + 9 < -15
x + 9 > 15 or x + 9 < -15
-15 < x + 9 < 15

Question 8
Solve |6x + 8| > 4.
{x| -4 < x < 4}
{x| -2 < x < -2/3}
{x| x > -2 or x < -2/3}
{x| x > -2/3 or x < -2}

Question 9
Which of the following has the solution shown on the number line?

|x + 3| ≤ 2
|x – 3| ≤ 2
|x + 3| ≥ 2
|x – 3| ≥ 2

Question 10
What is the solution of |x + 3| > -2?
x > 1 or x < -5
-5 < x < 1
all real numbers
no solution
• Aug 25th 2012, 03:16 PM
Plato
Re: Inequalities HELP!!
Quote:

Originally Posted by zales127
Need Help!!! This is not for a graded quiz. Im trying to tutor my son but Im no math wiz myself and need to figure out the correct answers so that I know when I try to help him!!!

Question 1
Which of the following is equivalent to |4x + 5| = 88?
-4x + 5 = 88
4x + 5 = -88
4x + 5 = 88
4x + 5 = 88 or 4x + 5 = -88

Question 2
Solve |6x – 5| = 25.
{5, -5}
{5, -10/3}
{-25, 25}
{10/3, -5}

Question 3
Which statement has the solution shown on the number line?

|x + 1| = 4
|x – 1| = 4
|x| = 3
none of the above

Question 4
Which statement is equivalent to |3x + 7| ≤ 30?
3x + 7 ≤ 30 or 3x + 7 ≥ -30
-30 ≤ 3x + 7 ≤ 30
3x + 7 ≤ 30
3x = 7 ≤ -30

Question 5
Solve |x+5| < 9.
{x| x < 4 or x > -14}
{x| x < 4 or x > -4}
{x| -14 < x < 4}
{x| -4 < x < 4}

Question 6
Which inequality has the solution shown on the number line?

|4 – x| ≤1
|x – 4| ≤ 1
|x + 2| ≥ 5
|x + 2| ≥ 7

Question 7
Which statement is equivalent to |x + 9| > 15?
x + 9 > 15
x + 9 < -15
x + 9 > 15 or x + 9 < -15
-15 < x + 9 < 15

Question 8
Solve |6x + 8| > 4.
{x| -4 < x < 4}
{x| -2 < x < -2/3}
{x| x > -2 or x < -2/3}
{x| x > -2/3 or x < -2}

Question 9
Which of the following has the solution shown on the number line?

|x + 3| ≤ 2
|x – 3| ≤ 2
|x + 3| ≥ 2
|x – 3| ≥ 2

Question 10
What is the solution of |x + 3| > -2?
x > 1 or x < -5
-5 < x < 1
all real numbers
no solution

Do not post a whole wish list of problems.
Usually no more than max of three.
Also include some of your own effort.
This is not a free homework service. It is a help service.
• Aug 25th 2012, 03:22 PM
zales127
Re: Inequalities HELP!!
Thats the problem..Id LOVE to give some effort..If I even knew where to begin I wouldnt be here.
• Aug 25th 2012, 03:27 PM
Plato
Re: Inequalities HELP!!
Quote:

Originally Posted by zales127
Thats the problem..Id LOVE to give some effort..If I even knew where to begin I wouldnt be here.

Do you have a textbook? Do you have class notes ?
If not, why not?
• Aug 25th 2012, 03:31 PM
zales127
Re: Inequalities HELP!!
My sons algebra teacher quit at the beginning of the year. He has struggled in math since he began school and unfortunately Im not much help. The school went through 11 substitutes in 1 year. The substitutes that they had bounced all over and no one really cared about the kids since it was a temporary job. 62% off the freshman class failed Algebra 1. In order to move on they have to take an online course for math that basically has a 5 minute tutorial on each subject. BUT if you dont understand the basics from subject to subject your pretty much screwed..which is where have 11 substitutes in 1 year left most of the kids!
• Aug 25th 2012, 03:51 PM
Plato
Re: Inequalities HELP!!
This is against our general policy. We are not suppose to do tutorials.
Say $K\ge 0$.
$\text{If }|ax+b|=K\text{ then }ax+b=K\text{ OR }ax+b=-K$

$\text{If }|ax+b|\le K\text{ then }ax+b\le K\text{ AND }ax+b\ge -K$

$\text{If }|ax+b|\ge K\text{ then }ax+b\ge K\text{ OR }ax+b\le -K$

EXAMPLES
$|3x+2|=5$ means $x=1\text{ OR }x=-\frac{7}{3}$

$|4x-5|\le 7$ means $-\frac{1}{2}\le x \le 3$

$|x+1|\ge 2$ means $x\le -3\text{ OR }1\le x$

BTW: If I were you I would file a lawsuit against the school system.
• Aug 25th 2012, 04:01 PM
zales127
Re: Inequalities HELP!!
Thank you!! This helps tremendously. We are in the works of taking action against the school right now with all the other parents.
• Aug 25th 2012, 04:34 PM
zales127
Re: Inequalities HELP!!
So if I have the problem |6x – 5| = 25

x=6 or 30/36...which I have a feeling is completely wrong
• Aug 25th 2012, 04:52 PM
Plato
Re: Inequalities HELP!!
Quote:

Originally Posted by zales127
So if I have the problem |6x – 5| = 25
x=6 or 30/36...which I have a feeling is completely wrong

$6x-5=25$ so $6x=30$ or $x=5$
OR
$6x-5=-25$ so $6x=-20$ or $x=\frac{-20}{6}$
• Aug 25th 2012, 06:59 PM
Prove It
Re: Inequalities HELP!!
Think of the absolute value as the "size" or "distance" of a number. For example |-4| = 4, since it is four units away from 0 on the number line, and |7| = 7, since it is 7 units away from the number line.

Also, in most of your questions, you have asked "which of these solutions is shown on the number line", without posting the number line in question...
• Aug 26th 2012, 07:52 AM
zales127
Re: Inequalities HELP!!
Thank you Prove It and Plato..I guess Im confused as to where - are the same. Like in this problem Which of the following is equivalent to |x - 2| = 6?
These are the options that I narrowed it down to..but I cant figure out where the - comes in.

x – 2 = 6
x – 2 = 6 or x – 2 = -6
By working the problem I think the answer is x-2=6 however it could be x-2=6 or x-2=16
• Aug 26th 2012, 07:59 AM
Prove It
Re: Inequalities HELP!!
Quote:

Originally Posted by zales127
Thank you Prove It and Plato..I guess Im confused as to where - are the same. Like in this problem Which of the following is equivalent to |x - 2| = 6?
These are the options that I narrowed it down to..but I cant figure out where the - comes in.

x – 2 = 6
x – 2 = 6 or x – 2 = -6
By working the problem I think the answer is x-2=6 however it could be x-2=6 or x-2=16

You are correct that it's both x - 2 = 6 and x - 2 = -6. That means x = 8 or x = -4.

This is easy to prove if you draw a number line and observe that 8 and -4 are both 6 units away from 2.
• Aug 26th 2012, 08:07 AM
zales127
Re: Inequalities HELP!!
Ok..i think Im slowly getting it. What does it mean when there is a line under < or >?
• Aug 26th 2012, 08:12 AM
zales127
Re: Inequalities HELP!!
Attachment 24603

The reason I asked the above question is because it states "Which of the following has the solution shown on the number line?

The answer that I came up with was |x + 1| ≥ 7
• Aug 26th 2012, 08:13 AM
zales127
Re: Inequalities HELP!!
Attachment 24603

The reason I asked the above question is because it states "Which of the following has the solution shown on the number line?

The answer that I came up with was |x + 1| ≥ 7 (Sorry the picture in my above post was really tiny..you have to click on the image)
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