Careless Algebraic Mistake

There are times when simple algebraic operations are confused by introducing trigonometric functions or logarithmic terms.

Example:

13 = 7 - 3x

This can be easily computed to be
13 - 7 = - 3x
==> 6 = - 3x
==> x = -2

But how about 13 = 7 - 3 tan X ?

Solution: 13 = 4 tan X ==> tan X = 13 / 4 , ..... and got into hot soup!

Why?

A careless mistake has been made.

When tan X was substituted into the original equation, the eyes refused to acknowledge this "complicated" tan X.
The eyes can only see the simpler "7 - 3" and thus compute it to be (7 - 3) = 4!

This caused the 7 - 3 tan X to be 4 tan X, which is WRONG.

The correct mathematical process of solving should maintain.

Therefore,

13 = 7 - 3 tan X
==> 13 - 7 = - 3 tan X
==> 6 = - 3 tan X
==> tan X = -2
.......

Maths is not that complicated when you follow the rules closely, even when the terms have changed into a seemingly complex expression / term.

By following what you have known with simple expression / term, any challenging equation can be easily solved.

This is the power of learning maths properly.
Being discipline in the way you handle maths is the key.

With a discipline mind, maths becomes fun , .. and interesting.

.