Solving First-Degree Equations

First degree or linear equations contain an unknown variable that needs to be found.

The variable can be a letter: x, y, z, a, etc ...

In a linear equation, the power of the variable is 1.

In order to solve a linear equations, we need to isolate the variable. This means that we need to get the

variable by itself on one side of the equal sign. Please see how this is done in the following examples.

To view an example, click on the word "Example":

Example 1: Solve 2x – 1 = 13

Example 2: Solve -7 = -5a + 9

Example 3: Solve 7x – 3 = 5x + 9

Example 4: Solve 4(y – 1) + 5(y + 2) = 3(y – 8)

Word Problems:

In order to solve work problems of this type it is helpful to use the following steps:

1. Read through the problem carefully and identify what you are trying to find. This is the unknown.

2. Assign a letter to the unknown. For example x = unknown quantity.

3. Read through the problem again and write an equation for x.

4. Solve the equation using the methods for solving linear equations.

To see some examples of how this is done, click on the word "Example": 

Example 5: If we subtract 27 from three times a certain number, the result is 18. Find the number.

Example 6: The sum of three consecutive integers is 13 greater than twice the smallest of the three integers. Find the integers.

Example 7: Khoa received a car repair bill for $106. This included $23 for parts, $22 per hour for each hour of labor, and $6 for taxes. Find the number of hours of labor.