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Fragile Dreams

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Dec 17, 2005
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Okay, following the advice of the elite, myself only a lowly noob....


(1) -12b < 0

I need to solve this inequality, but I'm dubious as how to as it's impossible- right???

(2) A supermarket manager wants to price a box of cereal. During a sale in which each box is marked off $1.50, the manager wants 5 boxes to sell for less than 3 boxes did before the sale. Write and solve an inequality to find the price the supermarket should charge for a box of cereal.

(3) (5 + r) - (6 - r) = 13


Argh, once agian I'd be ever grateful for any help.
 
1) -12b < 0

How would you solve "-12b = 0"? Use the same method, keeping in mind that you have to flip the inequality sign whenever you multiply or divide through by a negative.

2) A supermarket manager wants to prive a box of cereal. During a sale in which each box is marked off $1.50, the manager wants 5 boxes to sell for less than 3 boxes did before the sale. Write and solve an inequality to find the price the supermarket should charge for a box of cereal.

Reply from other thread: Assuming you mean "x" to stand for "the original price of one unit", then "5x" stands for "five times the original price", and "5x - 1.5" stands for "$1.50 off of five boxes". Is this what you meant?

Or should you find an expression for "$1.50 off one box"? And then create an expression for "five boxes at this new price"? And then set that "less than three boxes at the original price"?

And then you'd need to solve for the value of x, of course.

3) (5 + r) - (6 - r) = 13

Would it help to rewrite it thus?

. . . . .(5 + r) - 1(6 - r) = 13

Take the 1 through the parentheses, taking care with the signs. Then combine "like" terms on the left-hand side. Add "1" to both sides, and divide through by "2". Simplify to get the final answer.

If you get stuck, please reply showing what you have tried and how far you have gotten. Thank you.

Eliz.
 
G'day, Fragile Dreams.

(1)
Any positive number multiplied by -12 is going to be less than zero.

When we multiply (or divide) both sides of an inequality by a negative number, the direction of the inequality changes.

If -b < 0
then b > 0.
(divide both sides by -1 so the direction of the inequality changes).

(2) If x is the price of a box before the sale, then the price after the sale is (x - 1.5), right?
Now have another go.

(3)
You can think of -(6 - r) as -1(6 - r).
So just multiply out as we normally would:
-1 * 6 = -6
-1 * -r = r
So we have -1(6 - r) = -6 + r
Can you continue?
 
Eugh, do I feel like an idiot. I'm sorry, it's late and I'm tired and I nothing I read seemed coherent. Thank you so much, and yes I do believe I have it now.

Oh, and to stapel - Sorry, it is my first time here...
 
1) How are you getting "1"? How did the strict inequality become an "or equal to" inequality? Please show your steps.

2) Yes. Now solve the inequality.

3) Typo...?

Eliz.
 
(1) -12b < 0

Ans: b is greater than or equal to 1

Note: Apparently there's something wrong with this, as you say, seeing as I don't understand it...-I'm such a retard- Please, point out any misgivings.

(2) A supermarket manager wants to price a box of cereal. During a sale in which each box is marked off $1.50, the manager wants 5 boxes to sell for less than 3 boxes did before the sale. Write and solve an inequality to find the price the supermarket should charge for a box of cereal.

Ans: 5(x - 1.50) < 3x
x < 3.75

(3) (5 + r) - (6 - r) = 13

Ans: r = 7
 
1) I'll be glad to help you find your error, but you'll need to show what you did. From what I can see, you've somehow gotten that 0 ÷ -12 = 1. I don't know how you did that.

2) Yes. Now put units on the answer, appropriate to the word problem

3) To check the solution to any "solving" problem, plug the value back into the original equation and see if it works.

Eliz.
 
(1) *Sighs* Yes, my problem seems to be I don't know how to solve it I'm just guessing and checking. Would you explain it step-by-step please?

(2) Thanks, and yes I have done so.

(3) Yes, I've done so and it was correct.

I apologize for being the block-headed hassel I am, and for any inconvenience.
 
Fragile Dreams said:
(1) ...I don't know how to solve it...
Click to expand...
Have you not learned how to solve linear equations? (Linear equations are usually covered at length before getting to linear inequalities, but you don't seem familiar with the techniques, is why I ask.)

Eliz.
 
Well, let me see here...

-12b < 0

I assumed you would divide both sides by -12, but that isn't a possibility because you cannot divide 0 by any number

I'm dubious as to any other way
 
As I said in another post, zero divided by any non-zero number is zero.

0 / -12 = 0
 
-12b < 0

Divide both side by -12.

The direction of the inequality changes because we are dividing by a negative number.

b > 0/-12

and we have agreed that 0/-12 = 0 so we have

b > 0
 
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