Questions on Algebra: Operations with Signed Numbers answered by real tutors!

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Negative times negative equals positive.

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have a big proplem. I moved to Austia 2 years ago and i did not know german so i was not able to do the math. In school we are learning Pre algebra and i do not know a thing. if you can may you send me a couple of tipps and explainations to algebra
:
My advice to you is get a used pre-algebra book (in English) on Amazon or Alibris
they are very cheap. I have one (ISBN 0-395-74616-7) not too bad. Read, work the
problems, if you need it, you can submit specific problems here and someone will
explain it to you. The good thing is algebra is pretty much the same in any language.

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I recommend this site:
http://www.purplemath.com
.
It provides a great number of tutorials that covers the subject quite well.
.

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this is an order of operation problem:
3x2÷6+2x3÷6
??????? =
3²+2²+1²
------------------
QUestion: What are the instructions you have with this problem?
It is not clear what you are asked to do.
Cheers,
Stan H.

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a and b may be any integers, but c would have to be zero.
Cheers,
Stan H.

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I've tried this equation a few different ways, but I'm not coming up with the correct answer, please help.
[**The numbers beside the 't' are in subscript.][Note the dots are spacers to ensure the equation is in the correct format]

............KAT(t1 + t2)
If Q = -------------, solve for t
................d
-------------------
You show a t1 and a t2, but no t.

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-20 + 2k = k - 4k
-20 + 2k = -3k
-20 = -3k -2k
-20 = -5k
4 = k
hope uou will get it

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x/2 + 1 + 3x/4 = -9 first you would subtract -1 from both sides leaving x/2 +3x/4= -10 now multipy each term by 4 to get rid of your denominators 4(x/2) + 4 (3x/4) = -40 which when you simplify leaves you 2x + 3x = -40. Simplifying further by combining the x terms we have 5x = -40. Dividing both sides by 5 gives you x = -8
answer x = -8

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You gave us a[2a-4(2+a)] and said it is a fraction.
If so, where is the fraction?
I think this is a case involving the distributive rule.
In the brackets we have:
2a - 4(2 + a)....We simplify this first using the distributive rule to do away with the parentheses.
-4 times 2 = -8
-4 times a = -4a
We now have this in the brackets:
[-8 - 4a]
We now use the distributive rule again using the letter a outside the brackets.
a[-8 - 4a]
a times -8 = -8a
a times -4a = -4a^2
This is our answer: -4a^2 - 8a
==============================
If this is not what you want, then tell me where the fraction lies in your original question.

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-2/(-1/2)=-2*-2/1=4/4=4 Answer.

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.12(y-6)+.06y=.08y-.07(10)
.12Y-.72+.06Y=.08Y-.7
.12Y+.06Y-.08Y=-.7+.72
.1Y=.02
Y=.02/.1
Y=.2 ANSWER.
PROOF:
.12(.2-6)+.06*.2=.08*.2-.07*10
.12*-5.8+.012=.016-.7
-.696+.012=-.684
-.684=-.684

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what is the value of expressions?
15-3+2-9=?
17-12 = ?
5 = ?
==============
16+4:2+9=?
Comment: Your ":" confuses the problem.
Cheers,
Stan H.

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Hiking up a mountain, you notice that the air temperature drops 10 degrees C for every 1,000 meters increase in elevation. Write a multiplication expression to represent the decrease in temperature if you hike up the mountain 3,000 meters. Then evaluate the expression and explain its meaning.
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Let Tb be "temperature at the base of the mountain".
Let T(a) be "temperature at some altitude above the base".
Let a be the altitute above the base
------------
T(a) = T(b) - (a/1000)10
T(3000) = T(b) - (3000/1000)10
T(3000) = T(b) - 30 degrees
=================================
Cheers,
Stan H.

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order of solving is:
going from left to right
solve all expressions within parentheses first
-----
do exponentiation first
then mult/div
then add/subt
multiple occurrences of mult/div are done left one first.
multiple occurrences of add/subt are done left one first.
-----
your equation breaks down as follows:
-----
50 + (2*10) / 4 * 2 =
50 + 20 / 4 * 2 =
50 + 5 * 2 =
50 + 10 =
60
-----
the expression within the parentheses was done first.
since there was no exponentiation, the multiplication or division was done next going from left to right.
first was 2*10 within the parentheses which became 20
next was 20 / 4 which became 5
next was 5 * 2 which became 10
last was 50 + 10 which became 60
-----
answer would be 60.

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Whenever you multiply a negative with another negative number the product is always positive. (-)(-)=(+)
multiply (-)(+)=(-)
-9h=-3(-3)therefore-9h=(+)9
h=9/(-)9=-1

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9.1x-5=8.1x
9.1X-8.1X=5
X=5 ANSWER.

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Solve for A, A, R not = 0
A=(MX^3)/R
-----------------
A is already "solved for." ???

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Begin by subtracting 4 from both sides of the equation to get:
3x = 6
Divide both sides by 2 to get:
x = 3

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-7-(-5)*8 = -7-(-40) = -7+40 = -33

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Let's check your answer.

Your answer should look like n=...
Divide both sides by 4 to get,

If we plug that back in the original equation we get,
3(0-1)=5(0)+3-2(0)
3(-1)=3
-3=3
Your answer leads to a false statement.
Your answer is not correct.
.
.
.





This is an example of an inconsistent equation.
There is no "n" that makes this equation work.
There is no solution.

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2*5-6
10-6=4

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Find the difference of the given terms:
-15a squared b squared - (-6a squared b squared)
----------------------------------------------------
-15a^2b^2 - (-6a^2b^2)
= -15a^2b^2 + (6a^2b^2)
= -9a^2b^2
=============
Cheers,
Stan H.

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The problem is . I remember the order in which to solve issues, but not when to solve the in the equation.
-----------------------------
Do it first, so you get
.
X = 7/9 + 2
X = 2 7/9 or 25/9.
There are some ambiguities in the DEN, I assumed the -5 and the 7 were not in the DEN. It's not 100% clear.

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remember:
Let' see, given: , ,
So, , cross multiply

---------> the distance is CORRECT
Thank you,
Jojo

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-6.4-(-10.8)
= -6.4 + 10.8
= 4.4
==============
Cheers,
Stan H.

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jocelyn wants to estimate the cost per ounce of a 9.8 ounce jar of gravy that costs $2.75.
what would be a good estimate?
explain how you make this estimate.
-------------------------------------------
Estimate 2.75/10 = 27 cents
----------------------------
Actual: 2.75/9.8 = 0.2806.. or 28 cents
===========================
Cheers,
Stan H.

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Once you put a number inside the absolute value sign, it is made
positive no matter what it's sign is


answer

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Insert grouping symbols in the expression 2*3^3+4 to produce the indicated values: 4374 & 279,936. We figured out two of the other ones, but dont know what to do with these two.

Breaking 4374 down into primes:



So we can get the 7 by grouping (3+4)

so it's  2*3^(3+4) = 4374

-------------------------------------

Break 279936 down into primes:



We can write this as



And we can get the 7 by grouping 

So it's (2*3)^(3+4) = 279936

Edwin

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what is the perimeter of a rectangle with length of 7 and width of w?
------------------------------
Sketch it, and you'll see it's 2*7 + 2*w
=2w + 14

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Let's simplify this expression using synthetic division


Start with the given expression

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is -2


Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.

-2	|	2	-1	3	-1
	|

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)

-2	|	2	-1	3	-1
	|
		2

Multiply -2 by 2 and place the product (which is -4) right underneath the second coefficient (which is -1)

-2	|	2	-1	3	-1
	|		-4
		2

Add -4 and -1 to get -5. Place the sum right underneath -4.

-2	|	2	-1	3	-1
	|		-4
		2	-5

Multiply -2 by -5 and place the product (which is 10) right underneath the third coefficient (which is 3)

-2	|	2	-1	3	-1
	|		-4	10
		2	-5

Add 10 and 3 to get 13. Place the sum right underneath 10.

-2	|	2	-1	3	-1
	|		-4	10
		2	-5	13

Multiply -2 by 13 and place the product (which is -26) right underneath the fourth coefficient (which is -1)

-2	|	2	-1	3	-1
	|		-4	10	-26
		2	-5	13

Add -26 and -1 to get -27. Place the sum right underneath -26.

-2	|	2	-1	3	-1
	|		-4	10	-26
		2	-5	13	-27

Since the last column adds to -27, we have a remainder of -27. This means is not a factor of
Now lets look at the bottom row of coefficients:

The first 3 coefficients (2,-5,13) form the quotient



and the last coefficient -27, is the remainder, which is placed over like this





Putting this altogether, we get:



So

which looks like this in remainder form:
remainder -27

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Please post the entire problem so we can help you out.

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1. why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality?

This only applies when multiplying or dividing the inequality by a negative number. The inequality has to change because once you have done the operation you are dealing with a whole new range of numbers (on the opposite side of zero). Another way to look at it (if one side is positive and the other is negative) is that the greater/less than sign has to continue to face whichever side (or sign, negative or positive) it faced in the beginning at all times.
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2. what are the basic steps involved in problem-solving and what is the importance of following these problem solving steps when presented with a problem?

This depends on the problem. But for most problems, it is simple:
-identify what you are solving for before you jump into the equation(!*especially if there is more than one variable)
-set up an equation (if it's not set up already)
-isolate the variable

For word problems:
-express everything unknown in terms of a variable (or two or three, if necessary)
-set up an equation according to the information given in the problem

For some, like fractions, you have to:
-find the common denominator
-add or subtract as indicated
-factor(if possible)
-cancel (if possible)

For others, like quadratic, you have to:
-factor
-set equal to zero
-solve for variable

For some, like lines/inequalities, you have to:
-isolate y
-plug in coordinates(if possible) or
-graph (if already solved) including any shading

The steps you take don't ALWAYS have to be in the order that I presented them. As long as you don't LEAVE OUT any steps (doing them in your head is okay, that's not the same as leaving them out).

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6y-3y+2=-16
3y = -18
y = -6
=========
Cheers,
Stan H.

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divided by

Factor everything possible

divided by

Cancel everything in common

divided by

Now flip the second one

multiplied by

Then multiply



Simplify the mess



Take negative two out of the denominator



Cancel out like terms

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7-1+6=6+6=12

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Different-sized reantal trucks cost $19.99,$29.99,or $39.99 plus $0.10 per mile. Equations are for the total erntal cost,C, in dollars, for x miles driven.
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You basically have three different trucks that rent for a different cost:
If 'x' is "miles driven":
Then for the $19.99 truck:
C(x) = .10x + 19.99
.
Then for the $29.99 truck:
C(x) = .10x + 29.99
.
Then for the $39.99 truck:
C(x) = .10x + 39.99
.
Notice for each of the equations above, they are in the format of the "slope intercept" form of a line:
y = mx + b
where
m = slope
b = y-intercept
.
Notice that the "slope" (m) of each of the three equations are the same -- therefore, all three lines will be parallel.
.

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The problem is 54-6 divided by 2+6=?
(54-6) / (2+6)
= 48/8
= 6
========
Cheers,
Stan H.

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Start with the given expression.


Subtract from to get .


Multiply and to get .


Subtract from to get .


So

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5+4(2-6)-10+3
5+4(-4)-7
5-16-7
5-23
-18 answer.

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This expression is defined for all x except where that value of x makes the denominator 0.
So factor the denominator


When x equal 1 or x equal -5, the denominator is 0. Anything divided by 0 is undefined.

All values except 1 and -5

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X+8
________
X^2+4X-5
Determine the values of x where the expression is defined.
---------------
(x+8)/[(x+5)(x-1)]
Expression in undefined where the denominator is zero;
that is at x = -5 and at x = 1.
=======================
Cheers,
Stan H.

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Think of it this way.

Multiplication is an operation performed on two numbers. Visualize it as taking steps on the number line. You are going to take the number of steps specified by the first number, and each of the steps is going to be the second number long. So if you multiply 2 times 3, you are going to take 2 steps, each 3 units long.

Now, when you start to consider signed numbers, think of the sign on the first number as indicating the direction you are facing on the number line. That is, if it is positive you face to the right, and if it is negative, you face to the left. The sign on the other number tells you whether to walk forwards or backwards -- that is, either in the direction you are facing, or away from the direction you are facing.

Examples:
2 times 3. Face RIGHT and take 2 steps FORWARD, each 3 units long. You end up at 6.

-2 times 3. Face LEFT and take 2 steps FORWARD, each 3 units long. You end up at -6.

2 times -3. Face RIGHT and take 2 steps BACKWARD, each 3 units long. You end up at -6.

-2 times -3. Face LEFT and take 2 steps BACKWARD, each 3 units long. You end up at 6.