Linear Equation (One Variable)

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

Example 1

Example

x + 2 = 3 means [blank] + 2 = 3.

So solving an equation is
finding the value of the [blank],
which you've done before.

So the goal is to find the value of x.

Solution

To solve the equation, 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

x = 1
This is the answer.

Example 2

Example

Solution

The left side is x - 1.
So, 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

x = 9
This is the answer.

Example 3

Example

Solution

The left side is 7x.
So, 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

x = 5
This is the answer.

Example 4

Example

Solution

The left side is -x/4.
So, to remove the minus sign and the denominator 4, multiply -4 to both sides.
Then the left side is x.
And the right side is 9⋅(-4).

9⋅(-4) = -36

x = -36
This is the answer.

Example 5

Example

Solution

The x terms should be in the left side.
And the other terms should be 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
So 3x = -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

x = -7
This is the answer.