Equations Help?

Question

Could you show me how to solve the questions below?

1. -2x + 5 = 4x - 7

2. 12y + 4 = 8y - 12

3. 7z - 18 = -2z + 18

4. 10x + 15 = 5x - 10

Thank you very much.

Answer 1

There are basically only two things you should remember to solve all problems like this:
1) Since the equations are equal, anything you do to both sides will not change the equality (i.e. add, subtract, multiply, or divide the same number to both sides is ok).
2) The goal is to get x by itself on one side.

Let's try the first one:
-2x+5=4x-7
First you add 2x to both sides.
-2x+5+2x=4x-7+2x
The -2x and 2x on the left side cancels each other out. On the right side, they become 6x.
5=6x-7
Now add 7 to both sides.
5+7=6x-7+7
The 7's on the right side will cancel out. On the left side, 5 and 7 will make 12.
12=6x
Now divide both sides by 6.
12/6=6x/6
The left side becomes 2 and the right side becomes x.
2=x
So that's your answer.

Do the same thing for the other problems as an exercise. You'll know how to do these by inspection (in your head) eventually. Good luck.

Answer 2

Sure. here you go. I hope this helps
1. -2x + 5 = 4x - 7
(first u must get the x on one side and the indiviual numbers on the other) so u add 2x to each side and add 7 to each side. So it will look like.
-2x +2x + 5+7 = 4x + 2x -7+7
on the left the 2xs cancel each other and on the right the 7s cancels each other.
so u end up with:
12 = 6x
now you have to divide by 6 on each side (so u can get the x by itself).
12/6 = 6x / 6
so you end up with 2 = x
(I'm not going to write the others out, I did it to explain it on the first one)

2. 12y + 4 = 8y - 12
12y-8y +4 - 4 = 8y - 8y - 12 - 4
4y = -16
4y / 4 = -16 / 4
y = -4

3. 7z - 18 = -2z + 18
7z + 2z -18+18 = -2z + 2z +18 + 18
9z = 36
9z / 9 = 36 / 9
z = 4

4. 10x + 15 = 5x - 10
10x - 5x +15 - 15 = 5x - 5x - 10 -15
5x = -25
x = -5

I hope this helps. Any trouble feel free to email me. I'm in college to become a high school math teacher. So I can most likely answer most of the questions you have.

Answer 3

To solve any of these equations simply move all the terms with letterss to yje left side and all the numbers to the right side . Just remember that when you move a term from one side to the other, you must change its sign.

1. -2x + 5 = 4x - 7
-2x -4x=-7 -5
-6x=-12
x=2

2. 12y + 4 = 8y - 12
12y-8y = -4-12
4y=-16
y=-4

3. 7z - 18 = -2z + 18
7z+2z 18+18
9z=36
z=4

4. 10x + 15 = 5x - 10
10x-5x=-15-10
5x=-25
x=-5

See how easy. This process is called transposition, but it does not seem to be taught nowadays.

Answer 4

1.) -2x + 5 = 4x -7
-2x +12 =4x
12=6x
2 = x

2.) 12y + 4 = 8y - 12
4y + 4 = -12
4y = -16
y = -4

3.) 7z -18 = -2z +18
9z - 18 = 18
9z = 36
z = 4

4.) 10x + 15 = 5x - 10
5x + 15 = -10
5x = -25
x = -5


if you can't follow my math...feel free to email me. [e-mail]

i tried to go one step at a time

good luck

Answer 5

1. -2x + 5 = 4x - 7 add 2x to each side
5=6x-7 add 7 to each side
12=6x divide both sides by 6
2=x or
x=2

2. 12y + 4 = 8y - 12 subtract 8y from each side
4y+4=-12 subtract 4 from each side
4y=-16 divide both sides by 4
x=-4

3. 7z - 18 = -2z + 18 add 2z to each side
9z-18=18 add 18 to each side
9z=36 divide both sides by 9
z=4

4. 10x + 15 = 5x - 10 subtract 5x from each side
5x+15=-10 subtract 15 from each side
5x=-25 divide both sides by 5
x=-5

Answer 6

1. -2x + 5 = 4x - 7
-2x + 2x + 5 = 4x + 2x - 7
5 = 6x - 7
5 + 7 = 6x - 7 + 7
12 = 6x
12/6 = 6x/6
2 = x

2. 12y + 4 = 8y - 12
Taking the steps 2 at a time,
12y - 8y + 4 - 4 = 8y - 8y - 12 - 4
4y = - 16
4y/4 = - 16/4
y = - 4

The others can be solved in the same fashion.

Answer 7

The point to all these equations is to get the variable by itself.

step 1: -2x +2x + 5 = 4x+2x -7

step 2: +5 +7 = 6x - 7 +7 I'd rather work with positive numbers than negative ones

step 3: +12 /6 = 6x /6

step 4: 12/6 = x
step 5: 2 = x

The rest of the problems are like this one.

Answer 8

1)-2x + 5 = 4x -7
2)-2x -4x = -5 -7
3)-6x = -12
4)-6x/-6 = -12/-6
5)x = 2

1. equation
2.put like terms on either side of the equation, but changing the one you're moving from the other side to the opposite sign (4x = -4x)
3.simplify
4. 'undo' multiplication by dividing how many x's there are (-6) and whatever you do to one side, you do to the other.
5.the answer.
And my nephew won't stop bugging me so I can't do the rest but I think you can get it from here.
Good luck! n_n

Answer 9

in view which you have x AND x² interior the equation someplace, it extremely is a quadratic. you prefer to get it interior the kind: ax² + bx + c = 0 So our equation is: x² - 7x + 38 = 5x + 3 We in actuality in simple terms choose each little thing on the left edge of the equation, so enable's subtract 5x on the two factors: x² - 12x + 38 = 3 Now we subtract 3 on the two factors: x² - 12x + 35 = 0 we've a quadratic expression wherein a = one million, b = -12, and c = 35. There are 2 effortless techniques of fixing. one million) Factoring: (x - 7)(x - 5) = 0 x = 7 or 5 2) Quadratic formula x = (-b ±?(b² - 4ac)) / 2a = (12±?((-12)² + (-4)(one million)(35)) / (2*one million) =(12±?(a hundred and forty four - one hundred forty))/2 =(12±?(4))/2 = (12+2)/2 or (12-2)/2 = 14/2 or 10/2 = 7 or 5

Answer 10

1. -2x + 5 = 4x - 7
adding -4x+7
-6x+12=0
adding -12
-6x=-12
dividing by -6
x=2

2. 12y + 4 = 8y - 12
adding -8y+12
4y+16=0
adding -16
4y=-16
dividing by 4
y=-4

3. 7z - 18 = -2z + 18
adding 2z-18
9z-36=0
adding 36
9z=36
dividing by 9
z=4

4. 10x + 15 = 5x - 10
adding -5x+10
5x+25=0
adding -25
5x=-25
dividing by 5
x=-5