# How do you solve 27- 11x = x - 33?

Apr 11, 2018

$x = 5$

#### Explanation:

$27 - 11 x = x - 33$

You want the answer to be of the form x=?

So, start by "undoing" the part of the equation furthest away from the variable: in this case, $+ 27$ and $- 33$ are furthest away from the $x$ on both sides

1. For this explanation, we will "undo" the $- 33$ on both sides

$27 - 11 x + 33 = x - 33 + 33$

2. Then collect like terms

$27 + 33 - 11 x = x$

$60 - 11 x = x$

It should be noted that it is possible to start by "undoing" the $+ 27$ in a similar way

Now we want to have all the $x$'s on one side so that it can be of the form x=?

3. "Undo" the $- 11 x$ on both sides

$60 - 11 x + 11 x = x + 11 x$

4. Collect like terms

$60 = 12 x$

To "solve" the equation the answer must be a "singular" x=?

5. "Undo" the $12 \cdot x$ on both sides

$\frac{60}{12} = \frac{12 x}{12}$

6. Collect like terms and cancel appropriately

$5 = x$

Therefore

$x = 5$

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*Footnote*

In this context, "undo" means to "do the opposite of", so to "undo" a $- 2$ it is necessary to $+ 2$. However, this must be done on both sides of the equation in order to maintain its balance.

Eg: if 1kg was to be added to one side of a balance scale, the same weight must be added to the other side so that the balance is maintained.