How do you solve -10+x+4-5=7x-5?

1 Answer
Aug 26, 2016

First, you gather all the "x" terms on one side of the equation;

Explanation:

and all of the constants on the other side of the equation.

You have:
-10 + x + 4 - 5 = 7x - 5

1st: subtract x from both sides of the equation.
(We want to move the x over to the right-hand side, so we do the opposite operation on x. X is positive on the left, so we subtract, and we have to do the same thing to both sides of an equation.):

-10 + x + 4 - 5 = 7x - 5
.........- x...........- x

You then have:
- 10 + 4 - 5 = 6x - 5

All the x's are now on the right-hand side of the equation.

Now combine the constants on the left side of the equation:
- 10 + 4 - 5 = - 15 + 4 = - 11

so we have:
- 11 = 6x - 5

There is one more constant to move, so add it to both sides:
We have: - 11 + 5 = 6x , which is - 6 = 6x

Let's write it as:
6x = - 6

Now we need to divide both sides by - 6 in order to end up with only one x:
(6x)/ - 6 = - 6 / - 6,

which equals:
- x = 1

Since we want to know what positive x is, we now multiply both sides of the equation by - 1 to get:

x = - 1
which is the answer.

Now check by plugging - 1 back into the original equation:
- 10 - 1 + 4 - 5 = 7(- 1) - 5

Do both sides add up to negative 12? They should.