An equation is a mathematical equality between two algebraic expressions, such as: A = B. A **linear equations in one variable** it only involves adding and subtracting one variable to the **first power**. For example, 2x + 1 = 3 is a linear (or first degree) equation of one variable. Where:

- The first term is 2x + 1 and the second is 3.
- The coefficients 2 and 1 and the number 3 are known constants.
- x is the unknown and constitutes the value to be found for equality to be true. For example, if x = 1, then in the above equation we have:

2(1) + 1 = 3

2 + 1 = 3

3 = 3

**Solving linear equations with one variable**

- If present, remove parentheses and denominators.
- Group the variable terms in one member and the independent terms in the other.
- Reduce like terms.
- Clear the variable.

**Example 1**: Find the value of x from the following equation x + 2 = 7.

We group the variable terms in the first member and the independent terms in the other:

x = 7 - 2

By subtracting, we get:

x = 5

The value of x for the equation to have a solution is 5 (x = 6).

**Example 2**: Find the value of z from the following equation z - 4 = 8 - z.

We group the variable terms in the first member and the independent terms in the other:

z + z = 8 + 4

We reduce the like terms:

2z = 12

We clear the variable, for this we divide both members by 2:

2z / 2 = 12/2

z = 6

The value of z for the equation to have a solution is 6 (z = 6).

**Example 3**: Find the value of x from the following equation 5 (x + 1) + 3 (x - 2) = 2 (x + 2).

We first remove the parentheses by applying the distributive property in the necessary terms:

5x + 5 + 3x - 6 = 2x + 4

We group the variable terms in the first member and the independent terms in the other:

5x + 3x - 2x = 4 - 5 + 6

We reduce the like terms:

6x = 5

We clear the variable, for this we divide both members by 6:

6x / 6 = 5/6

x = 5/6

The value of x for the equation to have a solution is 5/6 (x = 5/6).