Solve for x?
E) 15-(x-6)=6-(3x+5)
First some rules. The ORDER OF OPERATIONS:
When expressions have more than one operation, we have to follow rules for the order of operations:
First do all operations that lie inside parentheses.
Next, do any work with exponents or radicals.
Working from left to right, do all multiplication and division.
Finally, working from left to right, do all addition and subtraction.
Please Excuse My Dear Aunt Sally" = Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
So, let's tackle E) 15-(x-6)=6-(3x+5)
Following the rules on order of operation we would eliminate the parentheses first
15 - (x - 6) = 6 - (3x+5)
becomes:
15-x+6 = 6 -3x -5
I assume you know that there is an unwritten 1 in front of each parentheses. I also assume you know a negative times a negative = a positive and a postive times a negative = a negative.
Now we have, 15 - x + 6 = 6 - 3x - 5
We want all variables, here x's, on the same side--the left hand side of the equation.
We do that by adding +3x to BOTH sides, because what we do to one side of the equation we do to both in order to keep the balance.
15 -x +3x +6 = 6 -3x+3x-5
15 +2x +6 = 6 -5
Now simple addition
15+6 +2x = 6 + (-5)
21 +2x = 1
To get the x variable alone on the left we add a minus 21 to BOTH sides
21 + (-21) +2x = 1 + (-21)
leaving
2x = -20
to get a single x divide through by two, BOTH sides
2x / 2 = -20 /2
x= -10.
Plug your answer in 15-(-10-6) =6 -(3*10 +5)
This is the how and the why. The rest follow the same pattern.
Hope this helps.
2007-11-04 11:59:57
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answer #1
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answered by dmontesmom2 4
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For most of the problems, don't forget the negative in front of the ( ...) changes the value of a negative to a positive and a positive to a negative, also don't forget the value with the negative number as you distribute it. I hope this helps. I only described the 1st 2 problems, since I'm sure that you will figure out the rest since it is done the same way.
e) 15-(x-6)=6-(3x+5)
15-x+6= 6-3x-5 {distributing the -1 in front of the () }
21-x =1-3x {adding the like terms together}
20 = -2x { dividing by 2 to find what x = by itself}
-10 = x
A) (8x-11)-(15-x)=1 {distributing the -1 in front of the () }
8x -11 -15 +x = 1
9x -26 = 1 { combining like terms}
9x = 27 {the variable one side & the number on the other}
x =3 {dividing by 9, to get the answer}
W) 2(x-5)-5x=8-3(5x-2)
2x - 10 -5x = 8 -15x +6
-3x - 10 = 14 -15x
12x = 24
x = 2
Q) 3(2x-3)-12=4(x-5)
6x -9 -12 = 4x -20
6x - 21 = 4x -20
2x = 1
x = (1/2)
U) 5-7(2-x)= 31-4(2x-5)
5 -14+7x = 31-8x+20
-9+7x = 51 -8x
15x = 60
x = 4
R)3(x+5)=21-4(x+5)
3x +15 = 21 -4x -20
3x + 15 = 1-4x
7x = -14
x = -2
O)3x+2(x+2)=13-(2x+2)
3x +2x +4 = 13-2x-2
5x+4 = 11 -2x
7x = 7
x =1
T) 2(x+4)+16=0
2x +8 +16 =0
2x = -24
x = -12
2007-11-04 11:52:00
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answer #2
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answered by pawdog530 3
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Haven't done this in a long time, but I do want to tell you that those above me who answered this problem were so rude. All of us need help sometime and math isn't always everyone's forte. Make sure you get some tutoring help before the test because we won't be there to answer your questions! Good luck!
E) 15-(x-6)=6-(3x+5)
15-x+6=6-3x-5
+x +x
15+6=6-2x-5
21=1-2x
-1 -1
20=2x
/2 /2
10=x
A) (8x-11)-(15-x)=1
8x-11-15+x=1
9x-26=1
+26 +26
9x=27
/9 /9
X=3
W) 2(x-5)-5x=8-3(5x-2)
2x-10-5x=8-15x+6
-3x-10=2-15x
+10 +10
-3x=12-15x
+15x +15x
12x=12
/12 /12
x=1
Q) 3(2x-3)-12=4(x-5)
6x-9-12=4x-20
6x-21=4x-20
+21 +21
6x=4x+1
-4x -4x+1
2x=1
/2 /2
X=0.5
U) 5-7(2-x)= 31-4(2x-5)
5-14+7x=31-8x+20
-9+7x=51-8x
+9 +9
7x=60-8x
+8x +8x
15x=60
/15 /15
X=4
R)3(x+5)=21-4(x+5)
3x+15=21-4x-20
3x+15=1-4x
-1 -1
3x+14=-4x
-3x -3x
14=-7x
/-7 /-7
-2=x
O)3x+2(x+2)=13-(2x+2)
3x+2x+4=13-2x-2
5x+4=11-2x
-4 -4
5x=11-6x
+6x +6x
11x=11
/11 /11
X=1
T) 2(x+4)+16=0
2x+8+16=0
2x+24=0
-24 -24
2x=-24
/2 /2
X= -12
2007-11-04 12:06:51
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answer #3
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answered by sadmom 2
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T) 2(x + 4) + 16 = 0
2(x + 4) + 16 = 0
2(x + 4) = <16> ; Distributive property
2x + 8 = <16> ; Distributive property
2x = <16> + <8> ; Distributive property
2x = <24> ; Addition
x = <24>/2 ; Distributive property
x = -12 ; solution.
{
2(<12> + 4) + 16 = 0
2(<8>) + 16 = 0
<16> + 16 = 0
0 = 0
}
2007-11-04 11:35:26
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answer #4
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answered by Anonymous
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What?
No I won't tell anyone but I'll only do one. You do the rest.
E) 15 - (x - 6) = 6 - (3x + 5)
1) remove the brackets by multiplying everything in the brackets by what is immediately outside the brackets - rhs. Here it is -1 on both sides of the equation.
-1 X (x - 6) becomes -x + 6 and -1 X (3x + 5) = -3x - 5
Putting the equation together you get
15 + x + 6 = 6 - 3x -5 ie 21 + x = 1 - 3x
solve the equation by adding 3x to both sides and subtracting 21 from both sides.
4x = -20
Therefore x = -5
Do the rest your self.
2007-11-04 11:28:57
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answer #5
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answered by jemhasb 7
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E)
15-(x-6)=6-(3x+5)
15-x+6=6-3x-5 cuz u carry the sign thru the ()'s
21+x=1+3x to collect common terms
-x -x
21=1+2x
-1 -1
20=2x
-10=x
A)
(8x-11)-(15-x)=1
8x-11-15+x=1
9x-26=1
+26 +26
9x=27
9x/9=27/9
x=3
W)
2(x-5)-5x=8-3(5x-2)
2x-10-5x=8-15x+6
-3x-10=14-15x
+3x +3x
-10=14-12x
-14 -14
-24=-12x
-24/-12=-12/-12
2=x
k im bored now,
do ur own flippin hw.
so just try doing them all like that,
and email if u dont get it
2007-11-04 11:41:53
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answer #6
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answered by lalala 3
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On all of those? Jeeze man, learn how to do your damn homework... Lazy little bastard.
E) 15-(x-6)=6-(3x+5)
15-x+6=6-3x-5
20-x=-3x
20=-2x
-10=x
W) 2(x-5)-5x=8-3(5x-2)
2x-5-5x=8-15x+6
-5=14-12x
-19=-12x
19/12=x
Q) 3(2x-3)-12=4(x-5)
6x-21=4x-20
6x-1=4x
-1=-2x
1/2=x
U) 5-7(2-x)= 31-4(2x-5)
-9+7x=51-8x
7x=60-8x
15x=60
x=4
R) 3(x+5)=21-4(x+5)
3x+15=1-4x
3x+14=-4x
14=-7x
-2=x
O)3x+2(x+2)=13-(2x+2)
5x+4=11-2x
5x=7-2x
7x=7
x=1
DISTRIBUTE. It's not that ******* hard.
2007-11-04 11:40:13
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answer #7
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answered by orbit_gum 1
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you need to distribute the number or sign outside to the paranthesis inside. i think that is what you are supposed to do, since you don't have the question???
2007-11-04 11:33:33
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answer #8
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answered by Mimi 2
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you are in so much trouble young man iam your teacher and youare getting a F
2007-11-04 11:28:52
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answer #9
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answered by Anonymous
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do your hw
2007-11-04 11:28:44
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answer #10
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answered by sexysaraxx 4
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