# Are These 2 Linear Equations Correct?

• Nov 4th 2012, 01:49 AM
MathClown
Are These 2 Linear Equations Correct?
The First One: 8(5-3x)-4(2+3x)=3

Expansion: -24x -12x 40-8 =3

Combine:-36x 32 =3

Shift: -36x = 3-32= -29

Solution: x= -29/-36

The Second One: 9(1+x)-8(x+2)= 2x

Expansion: 9x-8x 9-16 =2x

Combine: x -7 =2x

Shift: (x-2x) -7= 2x -2x

-x = -7

Solution: x= -7/-1

Is my formula for solving these equations correct (there are other ways but I thought my method is the easiest, or am I wrong?)? And are my solutions correct? If they're wrong, could you show me where I went wrong? Thanks guys!
• Nov 4th 2012, 01:59 AM
Prove It
Re: Are These 2 Linear Equations Correct?
These are very hard to read as you keep forgetting plus and minus signs! But your logic is fine. The first is correct. The second is not.

You are correct up to \displaystyle \begin{align*} x - 7 = 2x \end{align*}, now subtract \displaystyle \begin{align*} x \end{align*} from both sides to find \displaystyle \begin{align*} -7 = x \end{align*}.
• Nov 4th 2012, 01:15 AM
MathClown
Re: Are These 2 Linear Equations Correct?
Quote:

Originally Posted by Prove It
These are very hard to read as you keep forgetting plus and minus signs! But your logic is fine. The first is correct. The second is not.

You are correct up to \displaystyle \begin{align*} x - 7 = 2x \end{align*}, now subtract \displaystyle \begin{align*} x \end{align*} from both sides to find \displaystyle \begin{align*} -7 = x \end{align*}.

For the second one, WolframAlpha says the answer is x=7/-1???
• Nov 4th 2012, 01:16 AM
Prove It
Re: Are These 2 Linear Equations Correct?
Quote:

Originally Posted by MathClown
For the second one, WolframAlpha says the answer is x=7/-1???

Which is equal to -7...
• Nov 4th 2012, 01:21 AM
MathClown
Re: Are These 2 Linear Equations Correct?
Quote:

Originally Posted by Prove It
Which is equal to -7...

So WolframAlpha got it wrong? The final simplified answer is just x=-7? Is that what you're getting at? Or simply -7 since you're subtracting both x variables.
• Nov 4th 2012, 02:12 AM
Remember that when positive number is divided or multiplied by negative number, answer is negative. Wolfram alpha gave you $\frac{7}{-1}=-7$. So both Wolfram Alpha and Prove It are correct.