Solving Basic Algebra Question 1: x - (-6) = 12

[KevinMWHM]

1. x - (-6) = 12


To simplify, I want to get rid of the (-6). So wouldn't I say
2. x - (-6) +6 = 12 + 6
x = 18?


The book I'm using says to add (-6) to both sides but doesn't a neg + neg still equal a neg? I've been flawless to this point, what's confusing me?

The books answer
2. x - (-6) + (-6) = 12 - 6
x = 6

 

[Borek]

-(-6) + 6 = 6 + 6

 

[eumyang]

1. x - (-6) = 12


To simplify, I want to get rid of the (-6). So wouldn't I say
2. x - (-6) +6 = 12 + 6
x = 18?


The book I'm using says to add (-6) to both sides but doesn't a neg + neg still equal a neg? I've been flawless to this point, what's confusing me?

In the original equation a number is being subtracted from x. To isolate the x you need to add the same number.

If the equation was
$$x - 6 = 12$$
you would add 6 to both sides:
$$x - 6 + 6 = 12 + 6$$

But your equation is
$$x - (-6) = 12$$
which still has a subtraction, so you have to add (-6) to both sides:
$$x - (-6) + (-6) = 12 + (-6)$$

Another way to solve the equation is to first rewrite the subtraction as an addition:
$$\begin{aligned} x - (-6) &= 12 \\ x + 6 &= 12 \end{aligned}$$
Now that you have an addition, you subtract 6 from both sides to isolate the x:
$$x + 6 - 6 = 12 - 6$$

Hope this makes sense.


69

 

[AC130Nav]

1. x - (-6) = 12


To simplify, I want to get rid of the (-6). So wouldn't I say
2. x - (-6) +6 = 12 + 6
x = 18?


The book I'm using says to add (-6) to both sides but doesn't a neg + neg still equal a neg? I've been flawless to this point, what's confusing me?

The books answer
2. x - (-6) + (-6) = 12 - 6
x = 6

Your first step is to remove the parens by resolving -(-6), THEN you substract something from both sides of the equation.

 

[HallsofIvy]

Your first step is to remove the parens by resolving -(-6), THEN you substract something from both sides of the equation.

That is one way of doing the problem. You don't have to do it that way. eumyang showed how to do it following the OP's method.

 

[AC130Nav]

That is one way of doing the problem. You don't have to do it that way. eumyang showed how to do it following the OP's method.

But, perhaps, a student should be reminded to use the algebraic hierarchy. Makes it easier to understand.