It is easy to misuse the = when connecting parts of the argument—either putting them in when they do not belong or omitting them when they should be there.

Use = to connect expressions that are indeed equal to each other.

When the expressions all fit on a single line, generally the various forms are connected with an =.

As an example:

(3x + 2)(x − 4)  =  3x² − 12x + 2x − 8  =  3x² − 10x − 8.

Take care to use the same when writing this on multiple lines:

(3x + 2)(x − 4) =  3x2 − 12x + 2x − 8 =  3x2 − 10x − 8.

rather than:

(3x + 2)(x − 4) 3x2 − 12x + 2x − 8 3x2 − 10x − 8.

The following is correct, but somewhat harder to follow:

(3x + 2)(x − 4)  =
3x² − 12x + 2x − 8  =
3x² − 10x − 8.

Do not use = to connect equations or entities that are not equal to each other.

Correct symbols are &rarr or ⇒ (which can be read as "follows" or "implies") or ∴ (which is "therefore").

As an example:

2(x + 3)	= 6   →	x + 3	= 6   →  x + 3 = 12    ∴  x = 9
4		2

In this case, often the "arrows" are omitted when writing on separate lines:

2(x + 3)	= 6
4

x + 3	= 6
2

x + 3 = 12

∴  x = 9

When writing out the solution other arrows may be used to good advantage to show how pieces and parts may connect.

  (x − 2)(x + 5) = 0
       ↓         ↓
∴ x = 2,  x = −5

It is also helpful to add a word or two of description as to what is being done especially when it involves some "not so obvious" steps or combinations. As an example:

2(x + 3)	= 6
4

Cancelling

x + 3	= 6
2

Clearing fractions—multiplying both sides by 2

x + 3 = 12

∴  x = 9

Write clearly and accurately.

x − 1	+	x + 3
x		x + 2

To simplify this we need to multiply the first fraction, top and bottom, by x + 2 and the second by x. If you are not careful this might appears as:

x + 2	•	x − 1	+	x	•	x + 3
x + 2		x		x		x + 2

So far, so good. However, when rewriting this, parentheses are needed:

(x + 2)•(x − 1)	+	x•(x + 3)
(x + 2)x		x(x + 2)

Sometimes, without being careful one or more sets of parentheses are forgotten:

x + 2•(x − 1)	+	x•x + 3
(x + 2)x		x(x + 2)

The result is that sooner or later the numerator of the first fraction becomes x + 2x − 2 = 3x − 2 rather than the correct x² + x − 2. And the second numerator ends up as x² + 3 instead of x² + 3x.