# Linear Equations (One Variable)

How to solve linear equations (one variable) problems: examples and their solutions.

## Example 1

Solving an equation is finding the value of *x*

that makes the equation true.

So just think *x* + 2 = 3

as □ + 2 = 3.

We all know that □ = 1.

Solving an equation is that simple.

Then let's see, rather than just guessing the *x*,

how to find the value of *x* systematically.

To remove 2 on the left side,

write, the opposite of +2, -2 on both sides.

Then *x* = 3 - 2,

so *x* = 1.

This is the answer.

To check the answer,

put the answer into the *x*

and see if the equation is true.

1 + 2 = 3

is true.

So *x* = 1 is the right answer.

## Example 2

To remove -1 on the left side,

write +1 on both sides.

## Example 3

To remove the coefficient 7,

divide 7 on both sides.

## Example 4

To remove both (-) sign and 7,

multiply (-7) on both sides.

## Example 5

To solve this equation,

you should move +2*x* on the left side

and move +8 on the right side.

But, instead of writing -8 and -2*x* on both sides,

use this trick to solve the equation faster:

Move +8 to the other side

and change its sign (-8).

By the same way,

move +2*x* to the other side

and change its sign (-2*x*).

This trick will surely save your time

when solving equations.

To remove the coefficient 3,

divide 3 on both sides.

## Example 6

To solve the parentheses,

first mutiply [-3] and [*a*] (blue),

then multiply [-3] and [-2] (purple).

Move +6 to the right side

and change its sign (-6).

To remove the coefficient -2,

divide -2 on both sides.