How do you solve 2x+18+4x=-2x+10?

Mar 26, 2017

Add like terms, invert terms by switching their signs, add like terms again, and isolate for $x$. As a result, you get $x = - 1$.

Explanation:

Ultimately, we are to isolate $x$, in order to determine its value.

First off, what we have to do is to add like terms, making the equation easier to work with.

$2 x + 18 + 4 x = - 2 x + 10$

$18 + 6 x = - 2 x + 10$

That's as far as we can go. However, we can bring some terms to the other side of the equal sign. So let's do that in such a way where all like terms are on one side of the equal sign. When doing this, you must invert the value: negatives become positive and vice versa.

$6 x + 2 x = - 18 + 10$

Now, we can add like terms once more.

$8 x = - 8$

Finally, we can isolate $x$. To do this, we divide $8 x$ by $8$, in order to "cancel" the coefficient.

$\frac{8 x}{8} = - \frac{8}{8}$

$x = - 1$

As a result, we get $x = - 1$. We can double check our work by subbing in $x = - 1$ in the original equation.

$2 x + 18 + 4 x = - 2 x + 10$

$2 \left(- 1\right) + 18 + 4 \left(- 1\right) = - 2 \left(- 1\right) + 10$

$- 2 + 18 - 4 = 2 + 10$

$12 = 12$

As you can see, both sides of the equal sign are equal to each other. Therefore, we can conclude that $x = - 1$.

Hope this helps :)