Solve 8 - 4X = -5x + 18 Please tell me where I am making my mistake?

8 - 4x = -5x + 18
5x - 4x = -8 + 18
x = 10

8 - 4x = - 5x + 18
5x - 4x = 18 - 8
x = 10

others have already solved it for you, but I can tell you your mistake is in the first line. the equation you gave us is "8-4x" and then when solving it you wrote "4x-8." Big difference!

Your mistake is that the question is 8-4x=18-5x not 4-8x=18-5x
The correct solution would be
8-4x=18-5x
5x-4x=18-8
x=10

Hi Cak,

I will not tell you your mistakes in solving the problem but rather I would share to you better techniques in solving equation like this. Many students were used to add or subtract variables or constants to the left or the right of the equation. This method is confusing sometimes specially when many variables with powers and constants exist in the equation.

But there is an easy method in order to solve this kind of equation. I call this as "The Transposition Method". Rule: If you transpose variables or constants to either side of the equation, be sure to change their algebraic sign(s) i.e., from (+) to (-) and vice-versa

I will take your problem as an example;
The given equation was originally written like this;
8 - 4x = -5x + 18

Since you are solving for x, you are going to transpose all variables at the left side, and all constants at the right side of the equation.

Hence
- 4x + 5x = 18 - 8

Observe how I transposed terms to the left and the right sides of the equation. I changed the sign of -5x to +5x when I transposed it from the right to the left side; I changed the sign of 8 to -8 when I transposed it to the right side; and I retained -4x and 18 to their proper places because there is no need to transpose them. Remember always, everytime you transpose a variable or constants to another side , change their algebraic signs.

So, you are now ready to perform the indicated operations which is to add or to subtract like terms

- 4x + 5x = 18 - 8
x = 10 ----------------------->>> answer

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Notice in your second step that says:

4x-5x-8=-5x- -5x+18 ..... you put -5x = --5x, the left side should be the same, --5x not -5x. (this is +5X, also)

In other words you subtracted 5x from the left and added 5x to the right .... NOT BALANCED.

The rest look good algebraically but are wrong because of the mess up before. Peace.

8-4x = -5x +18
(+5x onto each side)

8+X=18

(minus 8 from both sides)
X = 10