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Combine like terms. Since 7x and -3x both contain an x, you can subtract them normally. 7x-3x=4x
You're then left with 4x=80
You want want to get x alone.
Divide each side by 4.
You're left with x=20.

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What can we use for the value of of dimes? .10x
(since times are worth .10 and we don't know how many we have, so we multiply x amount of times.
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What can we use for the value of quarters? .25(73-x)
(since we know quarters are worth .25 and all we know about how many we have is that there is 73 minus however many dimes we have. since we used x for the amount of dimes, we subtract x)
Now we set it all equal to the total amount
.10x+.25(73-x)=14.50 (We add just like if we're trying to find the value of 10 times and 10 quarters. We would do .10*10+.25*10=___)
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Solve for x. Remember what did we decide x was? the amount of dimes.
.10x+.25(73-x)=14.50 (distribute .25 to the numbers inside of parenthesis)
.10x+18.25-.25x=14.50 (combine like terms on each side)
-.15x+18.25=14.50 (subtract 18.25 from each side)
-.15x=-3.75 (divide each side by -.15 to get x alone)
x=25
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There are 25 dimes.
If you're unsure subtract 25 from 73 to get the amount of quarters.
Multiply the values out and add them up to see if they equal 14.50
73-48=48 quarters
25*.10+.25*48= 14.50 CHECK!
---------------------------------
answer=25 dimes

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Area of a circle= 3.14(radius^2)
(3.14)(5^2)
(3.14)(25)= 78.5mm

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x+(x+1)+(x+2)
x= the first number, and since we need consecutive integers, the next number will be x+1, and the next x+2.
So set this equation=-114
x+x+1+x+2=-114 (combine like terms)
3x+3=-114 (subtract 3 from each side)
3x=-117 (divide each side by 3)
x=-39
(now add one to this to get our 2nd number, and 1 more to get our third)
-39+1=-38
-38+1=-37
Now check to make sure it works!
-39+(-38)+(-37)=-114 CHECK!
ANSWER=-39,-38,-37

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Subtraction in this case means distribute the negative.
So we now have 2t-7-3t-5
Combine like terms
-t-12

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Read carefully and set up an equation.
sum of 6 and twice a number= 6+2x
7 less than a number = x-7
Since these two are said to be equal,
set them equal to each other and solve for x
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6+2x=x-7 (subtract x from each side)
6+x=-7 (subtract 6 from each side)
x=-13
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Now that we have the value of x,
replace x in the original equation and solve.\
6+2x=x-7
6+2(-13)=-13-7
6-26 =-20
-20=-20 CHECK!
-------------------------------
answer=-20

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We want to get the absolute value by itself
5(5x+7)+2<=21 (Subtract 2 from both sides)
5(5x+7) <=19 (Divide each side by 5)
5x+7 <=19/5 (Now we need to solve for both 19/5 and -19/5
-19/5<=5x+7<=19/5 (You can either set up two separate problems or build a 3 part problem.)
We need to get x alone.
Whatever you do to the middle to get x by itself, needs to be done to each side as well.
-19/5<=5x+7<=19/5 (subtract 7 from each side. Be sure to multiply 7/1 by 5 so you can get a common denominator and be able to subtract properly)
-54/5<=5x<=-16/5 (Now we need to divide each side by 5 to get x alone. Remember to divide by fractions, take the reciprocal and multiply- So we will be multiplying the left and right side by 1/5)
-54/25<=x<=-16/25
X is greater than or equal to -54/25
X is less than or equal to -16/25

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distribute.
2x (x+10) = 2x^2+20x
-3 (x+10) = -3x-30
Then put it all together,combining like terms in descending order.
ANSWER=
2x^2+17x-30

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First check to see if you can factor.
You can in the denominator.
Take the greatest common factor which is 6 in this case
The denominator should then look like this: 6(x-3)
If this looks confusing, distribute it back out and you will see that it equals the same thing.
Now we have: 12/6(x-3)
You can reduce since we have 12 and 6 in the problem.
Cancel out the 6 and make the 12 a 2.
Final answer= 2/x-3

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area of a square= length*width
area of a circle= Pi(3.14)*radius^2

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What can we use to represent the value of the width at this time?
Since we have no numerical value at this time, we'll use "x."
And what can we use for the length at this time?
Well we know that the length is 7ft longer than 2 times the width.
So we can represent this by 2x+7.
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We know that perimeter is the sum of all the sides.
In the case of the rectangle we can assume that perimeter equals 2 times the length+ 2 times the width.
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So with this information, let's set up an equation to solve for x
2x + 2(2x+7)=110 <--------- 2WIDTH+2LENGTH=PERIMETER
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Solve for x!
2x+2(2x+7)=110 (Distribute the 2)
2x+4x+14=110 (Combine like terms)
6x+14=110 (Subtract 14 from each side)
6x=96 (Divide each side by 6)
x=16 <-------What does this x represent? The value of the width!
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Now remember to always check what specifically the word problem is asking of you.
We want to know the value of the length, so we're not done yet.
So now we need to plug in the value of x into what we originally represented length to equal which was (2x+7)
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2(16)+7
32+7
39<------------------the value of the length!
---------------------------------------
Not sure if this is right? Check by adding up all the side of the values of width and length and see if they equal the given perimeter value.
39+39+16+16=110 CHECK!

ANSWER=
LENGTH=39ft

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I always recommend drawing a picture for problems like these.
--------------------------
What can we use to represent the value of the width right now?
Since we can not answer with a numerical value at this time, it is "x."
--------------------------
What can we use to represent the value of the length at this time?
Since all we now is that it is 8 ft longer then the width, we can represent it as "x+8"
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Since we also know the value of the perimeter...how can we solve to find the value x to solve for length and width?
Since we know Perimeter is the value of all the sides added up, we can conclude in the case of a rectangle that the value is 2 times the width +2 times the length.
-------------------------
Now, set up a problem to determine x using all the information we currently have.
What did we use for width- x
and length?- x+8
_---------------------------
Now lets use that 2 times length + 2times width= perimeter to figure out what x is!
2x+ 2(x+8)= 184 (distribute the 2)
2x+2x+16=184 (combine like terms)
4x+16=184 (subtract 16 from both sides)
4x=168 (divide by 4)
x=42
Now what does this x represent? The value of the width!
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Now how do we know what the length is?
Plug the value of x (42) into what we originally represented the length by which was(x+8)
42+8= 50
----------------------------
Not sure if this is right? add it all up to see if it equals the perimeter.
42+42+50+50=184. CHECK!
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Now remember with word problems, sometimes you have to do some extra work. Always make sure you answered what was originally asked.
So we're not done yet!
We want to know the area, and now that we know the value of the length and width, we can do that.
-------------------------------
Area= L*W
42*50=2100

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We need to get rid of the i's in the denominator.
You do this by multiplying the top and bottom by the conjugate of the denominator.
The conjugate of 6-9i is 6+9i.
You just need to change the sign of the second number.
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So lets multiply the numerator first.
(3-9i)(6+9i)= 18+27i-54i+81i^2
REMEMBER- i^2 is equal to -1. So replace the i^2 with -1
Multiply 81 by -1
= 18-27i-81
-63-27i <----------THIS IS OUR NUMERATOR FOR NOW
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Now, lets multiply the conjugate by the denominator
Remember the goal is to get rid of all i's in the denominator.
(6-9i)(6+9i) =36+54i-54i-81i^2
(i's cancel and we're left with only an i^2 which we now know needs to be replaced with negative 1)
=36-(81*-1)
=36+81
=117 <-----------------THIS IS OUR DENOMINATOR FOR NOW.
----------------------------------------
Now let's put them together in complex form which is a+bi.
This simply means numbers on one side and all numbers attatched to an i on the other
NOT IN COMPLEX FORM ANSWER= -63-27i/117
Since out denominator is 117, all numbers need to be over 117, but broken up so i's are to the right.
ANSWER IN COMPLEX FORM= (-63/117)-(27i/117)

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Question 1-
Since x is greater that or equal to 9, you would use a shaded circle on 9 and have it pointing to the right since those are the numbers greater than 9.
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So the answer would be: the wrong way to do it is: shading to the left
Question 2-
Get all numbers on one side and all x's one side.
-6x-10>14+ 2x (add 10 to both sides)
-6x>24+2x (Then subtract 2x from both sides)
-8x>24 (Then divide each side by -8 so we can get x alone)
REMEMBER- With inequalities, whenever you divide by a negative number, you have to flip the direction of the sign.
x<3

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2x^2-3x^2-3x+48 Combine like terms
-1x^2-3x+48 I find it easier to work with a leading coefficient of positive one, so I would switch the signs of every number
x^2+3x-48 Then look and ask yourself, what two numbers multiply to be -48 but when these two numbers are added, they add up to be 3.
These numbers are 8 and -6.
8*(-6)=-48
8+(-6)=3
ANSWER=
(x+8)(x-6)
If you're ever unsure if your answer is correct, foil your factoring back out and see if it equals the equation before you factored.

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I always recommend drawing a picture for word problems like this.
What can we say the width equals at this point? It is X
What can we say about the length at this points? It is 2x
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Perimeter=the sum of all the sides.
So at this point the information we have is 2x+2x+x+x
(since all we know about the side is x(we don't know this value) and that the length is two times as long (2x)
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Set up the equation with all the information we currently have
2x+2x+x+x=360 (combine like terms)
6x=360 (divide 6 on both sides to get x alone)
x=60
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With this information, we now know the length and width.
Width=60
Since we had our length as 2x. Multiply 60 by 2
Width=60
Length=120
---------------------------------------------------
If you want to check add it all up!
60+60+120+120=360

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Since you see x=11-3y, you will take what x equals (11-3y) and replace x in the other with this to solve for y.
---------------------------
Take 6x+5y=1
Replace x with (11-3y)
6(11-3y)+5y=1 (distribute 6)
66-18y+5y=1 (combine like terms)
66-13y=1 (get the term attached to y by itself. subtract 66 from each side)
-13y=-65 (get y alone, divide both side by -13)
y=5
------------------------

Now that you have the value of y, you need to replace y in one of the equations to get the value of x.
6x+5(5)=1
6x+25=1
6x=-24
x=-4
------------------------
ANSWERS=
x=-4
y=5

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Read through and try writing it out in numbers
"Four times"- We know we're multiplying something by four
"the sum of y and 3"- We now know what we're multiplying four by (y+3)
4(y+3)=-1 If you need to solve...
4y+12=-1 (distribute 4. 4*y and 4*12)
4y=11 (subtract 12 from both sides)
y=11/4 (divide each side by 4 to get y alone)

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Multiply (-7) by (-4)
This equals 28
(Remember-a negative multiplied by a negative=positive)
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Multiply (x^3) by (x)
This equals x^4.
(Remember-When multiplying exponents, the exponents are added.)
Now simply put these together and you get your answer
ANSWER=28x^4

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Start with the age you know and work backwards.
You know that Jim is 12.
Sarah is 2 years younger than Jim- so we now know she is 10.
Allen is 3 times as old as Sarah. 10*3=30
---------------------------------------------------
Allen is 30

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Area= Length * width
You are given the length as 8.
Since it states that the width is half of the length, this means the width is 4.
Area= 8*4=32in
-------------------------------------------
Perimeter= the sum of all the sides.
P=8+8+4+4=24 inches
---------------------------------------------
ANSWERS=
Area= 32in
Perimeter=24in

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Your values for x and y were not correct.
What I did was manipulated one of the equations so that that x's could cancel and give us the value of y. After having the value of y, we can plug that into one of the ORIGINAL equations and solve for x.
I multiplied (2x+5y=-16) by -3.
The problem now reads -6x-15y=48
So we now have the two equations:
-6x-15y=48
6x- 9y=-48.
Now add the two together to solve for y.
The x disappears since (-6x+6x=0)
We are left with -24y=0
Divide each side by -24, and you get:
y=0
Now that you have the value of y, take one of the ORIGINAL PROBLEMS and plug in the value of y.
So let's take 2x+5y=-16 and plug in the value of y (which is 0 in this case)
2x+5(0)=-16
2x=-16 divide each side by 2
x=-8

ANSWER=
X=-8
Y=0

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To solve for x, you want to get x by itself, which will give you the value of x.
23x=96. Is like saying 23 multiplied by some number equals 96.
So for us to be able to get x by itself, we need to do the opposite operation being performed by x.
Since we're multiplying in this case, we need to divide.
But remember, whatever you do to one side YOU MUST do to the other.
Therefore divide each side by 23.
The one side cancels leaving only x, while the other gives you the value of x
23x/23=96/23
x=96/23 (96 over 23)
Always be sure to put fraction answers into lowest terms.
In this case, 96/23 can not be reduced any further.

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The goal is to eliminate the denominators.
You should first make sure you can not factor anything, and then proceed.
Find the common denominator (every number/polynomial in the denominator must be represented)
In this case our common denominator is (2x-3)(x+2)
Multiply each side by (2x-3)(x+2)
Since (7/x+2) already contains x+2, these cancel, and you only multiply
7(2x-3)= 14x-21
Likewise with 4/2x-3. The 2x-3 on the denominator cancels and you multiply 4(x+2)= 4x+8
At this point your problem should look like this:
(14x-21)- (4x+8).
Since we have subtraction, we treat the negative sign like distributing a -1.
We then have:
14x-21-4x-8
Condense:
10x-29
Always check to see if you can further factor.
In this case, you can not.
Answer=10x-29

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This means wherever you see the letter x, you replace it with (3x-8) since that is the given function.
Therefore it would be set up:
4(3x-8)+20=0
Next, distribute (multiply 4(3x) and 4(-8)
12x-32+20=0
(-32+20 can be condensed)
12x-12=0
Now you want your x's on one side, and numbers on the other.
This is done by adding 12 to both sides so it cancels on one side, and transfers over to the other.
12x=12
Finally, we want x by itself to determine what its value is.
This is done by dividing by the number attached to the x.
And remember, whatever you do to one side, needs to be done to the other.
Therefore, divide both sides by 12
x=1