I need help with these equations?

Question

please dont just give me answers please explain......
and step-by-step

15 + 4x = -x + 10

&


4(2x - 6) = x + 2


&


2(x+5) + 1 = 3 (x - 1) + 4


&



- 3n + 12 + n = 22

Answer 1

15(-10) +4x = -x +10(-10)
5 +4x(-4x)= -x+(-4x)
5= -5x
x= -1

4(2x - 6) = x + 2
8x (-x)- 24= x (-x) + 2
7x - 24 (+24)= 2(+24)
7x =26
x = 3.7

2(x+5) + 1 = 3 (x - 1) + 4
2x+10 +1=3x-3+4
2x+11=3x+1
10=x

- 3n + 12 + n = 22
-2n +12 = 22
-2n= 10
n= -5

Answer 2

If you want to bring a number/algebra from the RHS to the LHS or vice versa,just mutiply it by -1.
For example,
a+b=c
a=c-b (Note the change of sign for b)

1: 15+4x= -x+10
5x= -5
x= -1

2: 2(x+5) +1 = 3(x-1) +4
2x+10 +1 =3x-3 +4
2x+11 = 3x+1
x=10

3: -3n + 12 + n =22
-2n = 22 - 12
-2n = 10
n= -5

You probably need help for shifting of the numbers/algebra.

Answer 3

15 + 4x = -x + 10
4x +x = 10 - 15 *'+' become '-' when change side, vice-versa.
5x = 5
x = 1

4(2x - 6) = x + 2
8x - 24 = x + 2
8x - x = 2 + 24
7x = 26
x = 26/7

2(x+5) + 1 = 3 (x - 1) + 4
2x + 10 + 1 = 3x - 3 + 4
2x - 3x = -3 + 4 - 10 - 1
- 3x = - 10
x = 10/3

- 3n + 12 + n = 22
- 3n + n = 22 - 12
- 2n = 10
n = -10/2
n = -5

Answer 4

15 + 4x = -x + 10
-15 + x +x - 15 (add/subtract)
5x = -5
5 5 (divide)
x = -1

4(2x - 6) = x + 2
8x - 24 = x + 2
-x +24 -x +24 (add/subtract)
7x = 26
7 7 (divide)
x= (26/7)

2(x+5) + 1 = 3 (x - 1) + 4
2x + 10 + 1 = 3x - 3 + 4
2x + 11 = 3x +1
-2x -1 -2x -1 (add/subtract)
10 = x

- 3n + 12 + n = 22
- 2n + 12 = 22
- 12 -12 (add/subtract)
- 2n = 10
-2 -2 (divide)
n = -5

Answer 5

15 + 4x = -x + 10
15-15+4x+x= -x+x+10-15
5x= -5
x= -1

4(2x - 6) = x + 2
8x-24=x+2
8x-x-24+24=x-x+2+24
7x=26
x=26/7


2(x+5) + 1 = 3 (x - 1) + 4
2x+10+1=3x-3+4
2x+11=3x+1
2x-2x+11-1=3x-2x+1-1
10=x


- 3n + 12 + n = 22
-2n+12-12=22-12
-2n/-2=10/-2
n= -5
I added all the steps because I wasn't sure what you leave out.

Answer 6

what youre trying to do in each of these is to solve for the value of some unknown (like x or n). you want to get this unknown variable by itself so your answer will be x= ? or n=?

1) 15+4x= -x+10

i would subtract 15 from both sides of the equation to get 4x by itself

15-15+4x= -x+10-15
4x= -x-5

now add x to both sides to get all x values on the left side of the equation

4x+x = -x + x -5
5x = -5

if you divide both sides by 5 you get

x = -1

2) 4(2x-6) = x + 2
when you have a number next to brackets, this means you have to multiply the number OUTSIDE the brackets by all amounts INSIDE the brackets.

here you have to multiply 4 across the brackets to get 4* 2x and 4* -6

8x-24 = x+2

and solve like before. subtract 'x' from both sides to get the x's on the left side of the equation. then add 24 to both sides to get:

8x-x-24 = x-x+2
7x-24 = 2
7x = 26

divide both sides by 7 to get x by itself
x = 26/7


3) 2(x+5) + 1 = 3(x-1) + 4
multiply across the brackets to get:

2x+10 +1 = 3x-3+4
2x+11 = 3x +1

combine the 'x's and numbers by subtracting 2x from each side and subtracting 1 from each side. note that it doesnt matter if you want to subtract 3x from each side or subtract 11. ultimately you end up with the same value.

2x-2x+11-1 = 3x-2x +1-1
10 = x


4) -3n + 12 +n = 22
combine the 'n' terms to get

-2n + 12 = 22
now subtract 12 from both sides

-2n + 12-12 = 22 - 12
-2n = 10
divide both sides by -2 to get 'n' by itself
n= -5


you just need practice. basically each example you do the same procedure.

Answer 7

1.15+4x=-x+10
add -15 to both sides
4x=-x+10-15
4x=-x-5
add x
5x=-5
divide by 5x=-1

2.4(2x-6)=x+2
remove thebrackets
8x-24=x+2
add 24
8x=x+26
add -x
7x=26
divide by 7
x=26/7

3.2(x+5)+1=3(x-1)+4
remove brackets
2x+10+1=3x-3+4
simplify
2x+11=3x+1
add -11
2x=3x-10
add -2x
0=x-10
add 10
x=10

4.-3n+12+n=22simplify
-2n+12=22
add -12
-2n=10
divide by -2
n=-5

Answer 8

Hi There
i will try to explain as simply as possible to you the method but you'll have to solve the equation by yourself;
let's begin with 4 very importants rules:
1- when we "move" any element in the equation from "left of the equal sign to its right" or from "right of the equal sign to its left", the sign of this element change. For instance let's take the following equation:
x + 1 = 2
"x" is now on the left of the equal sign. if we want to put that"x" to the right, we have to change its sign, and so we'll get:
1= 2-x
you can see that in the first one, there is no minus sign (-) before the"x",but in the second we added it.
if we do the contrary, we'll have to switch from "-x" to "x" . so basically we can say that:
" A POSITIVE (RESPECTIVELY NEGATIVE) ELEMENT BECOME NEGATIVE (RESPECTIVELY POSITIVE) WHEN HE CHANGE HIS POSITION IN THE EQUATION"
2-multiplying or dividing a negative number by a positive one gives us a negative one: [(-) x (+) = (-)]
3-multiplying or dividing a negative number by a negative one gives us a positive one: [(-) x (-) = (+)]
4-multiplying or dividing a positive number by a positive one gives us a positive one: [(+) x (+) = (+)]

That's for the rules, now the method to follow:
1st step:Try to eliminate all the "()" from your equation before beginning to solve it. to do that remember that for example:
2(5x+1) = 2 x 5x + 2 x 1, (to remove them, we have to multiply "2" per every element into the"()")
2nd step: Group all the unknowns in the same side (left or right of the equal sign). that means that if per example, we have the following equation:
12x +5 = 3-x ; we should right it like this:
12x+x=3-5 (don't forget Rule #1!!)

Now, let's solve the first equation:
15+4x= -x +10
let's group all the unknowns, we will get
4x+x = 10-15
and so we obtain:
5x = -5
thus:
x = -5/5
so finally
x = -1


I hope that you understood, bye!