How to solve algebraic equations in Excel? 7 - 3x = x - 4(2 + x)

[Guest]

I cannot determine how to solve algebraic equations in Excel, such as:
7 - 3x = x - 4(2 + x)

(This comes straight out of my daughter's 8th grade textbook. I'm no genius,
but I think it's actually reduces to x=0. Is that possible?)

I can create it in the Equation Editor, but can't do anything further with
it. (Can't even see it in a cell...)

Any solutions? Thanks for your help!

 

[JE McGimpsey]

One general way would be to express each half of the equation in
separate cells, using another cell (say, A1) as the variable, for
instance:

A1: 0
B1: =7 - 3*A1
C1: =A1 - 4*(2+A1)

Then set

D1: = C1 - B1

For the correct value of x (A1), D1 will = 0. With D1 selected, choose
Tools/Goal Seek. In the Goal Seek dialog, enter

Set cell: D1
To value: 0
By changing cell: A1

and click OK.

In this case the Goal Seek Status box will say "Goal Seeking with Cell
D1 may not have found a solution". This is because

7 - 3x = x - 4(2 + x)

is equivalent to

7 - 3x = x - 8 - 4x

or

7 - 3x = -8 - 3x or 7 = -8

which is not true for any value of x. So the "equation" is not an
equation after all...



ExcaliburMgtSolutions

 

[BenjieLop]

Why do you need Excel to solve your equation? You can do this algebrai
manipulation manually.

Let's start with your given equation

7 - 3x = x - 4(2 + x)

Expanding the right side of your equation

7 - 3x = x - 8 - 4x

... and simplifying

7 - 3x = -8 - 3x

Rearranging the terms,

- 3x + 3x = -8 - 7

0 = -15


... looks like the given equation is a mathematical fallacy as i
yields an answer of
0 = -15.

 

[Philippe L. Balmanno]

There is something wrong when you
7 - 3x = x - 4(2 + x)
7 - 3x = x - 8 - 4x
7 - 3x = -8 - 3x
- 3x + 3x = -8 - 7
0 = -15

--------------------------------------------------------------------------------

and JE McGimpsey
7 - 3x = x - 4(2 + x)
7 - 3x = x - 8 - 4x
7 - 3x = -8 - 3x or 7 = -8
come up with two different final answers.

I look at it as a formula that may be plotted so that if your x value is correct, plugging it in both sides of the equation should add up.

Value X 7 - 3x = 4(2 + x)
-15 52 = -52
-8 31 = -24
7 -14 = 36


Error detected in JE McGimpsey's solution however 52?-52 either.

 

[JE McGimpsey]

Phillippe - there aren't "two different final answers". The answers are
the same!

Subtract 7 from each side of

7 = -8

and you get

0 = -15

So there's nothing wrong with either analysis - the "equation" is simply
*not* an equation, because there are *no* solutions for x which will
result in a valid answer. It's a false statement, nothing more.


I gave you one method for using Goal Seek to solve an equation. However,
it only works if you use an actual equation, not a false statement.

 

[Dana DeLouis]

Another way to look at it would be if you were to plot both 7 - 3x , and
x - 4(2 + x), you would see that
they are parallel lines that do not intersect. (Both sides reducing to 7 -
3 x, and -8 - 3 x ).

 

[Philippe L. Balmanno]

Actually there was an error in reporting the final answer. But now I
understand what you meant.