Linear equations in one variable

linear equationAn 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

  1. If present, remove parentheses and denominators.
  2. Group the variable terms in one member and the independent terms in the other.
  3. Reduce like terms.
  4. 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).