# Linear Equation (One Variable)

How to solve a linear equation (one variable): 5 examples and their solutions.

## Examplex + 2 = 3

x + 2 = 3 means

[blank] + 2 = 3.

So solving an equation is

finding the value of the [blank].

So the goal is

to find the value of x.

To find the value of x,

the equation should look like

[x = ...].

But the left side is x + 2, not x.

So, to remove +2 in the left side,

move +2 to the right side.

When a term moves to the other side,

its sign changes.

Then the left side is x.

And the right side is

3,

change the sign of +2, -2.

3 - 2 = 1

So x = 1.

## Examplex - 1 = 8

The left side is x - 1.

To remove -1 in the left side,

move -1 to the right side.

When a term moves to the other side,

its sign changes.

Then the left side is x.

And the right side is

8,

change the sign of -1, +1.

8 + 1 = 9

So x = 9.

## Example7x = 35

The left side is 7x.

To remove 7 in the left side,

divide both sides by 7.

Then the left side is x.

And the right side is 35/7.

35/7 = 5

So x = 5.

## Example-x/4 = 9

The left side is -x/4.

So, to remove (-) and /4,

multiply (-4) to both sides.

Then the left side is x.

And the right side is 9⋅(-4).

9⋅(-4) = -36

So x = -36.

## Example5x + 8 = 2x - 13

Move the x terms in the left side.

And move the other terms in the right side.

So move +8 to the right side.

And move 2x to the left side.

Then the left side is

5x,

change the sign of 2x, -2x.

And the right side is

-13,

change the sign of +8, -8.

5x - 2x = 3x

-13 - 8 = -21

To remove 3 in the left side,

divide both sides by 3.

Then the left side is x.

And the right side is -21/3.

-21/3 = 7

So x = -7.