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# Math: Basic Tutorials

## One-Step Linear Equations

One-step linear equations are equations that only involve one operation (e.g. subtraction). This section explains how to solve this type of equation.

## Solving Equations Involving a Single Operation

Solving Equations Involving a Single Operation Video transcript - RTF

## Examples & Activity

### Examples

Click on the titles below to view each example.

Solve x minus 6 equals 8, and verify the solution.

Line 1: Add 6 to both sides so the equation is x minus 6 plus 6 equals 8 plus 6.

Line 2: Simplify to get the solution x equals 14.

Line 3: Check your answer in the given equation x minus 8 equals 8.

Line 4: Substitute x equals 14 into the equation, so it is 14 minus 6 equals 8.

Line 5: Simplify to get 8 equals 8

Since x equals 14 makes x minus 6 equals 8 a true statement, 14 is the solution to the equation.

Solve 13 equals 7 plus y, and verify the solution.

Line 1: Subtract 7 from both sides so the equation is 13 minus 7 equals 7 minus 7 plus y.

Line 2: Simplify to get the solution y equals 5

Line 3: Note that 5 equals y is the same as y equals 5.

Line 4: Check your answer in the given equation 13 equals 7 plus y.

Line 4: Substitute y equals 5 into the equation, so it is 13 equals 7 plus 5.

Line 5: Simplify to get 13 equals 13

Since y equals 5 makes x minus 13 equals 7 plus y a true statement, 5 is the solution to the equation.

Solve negative y equals 15, and verify the solution.

Line 1: Remember that negative y means negative 1y, so rewrite the equation as negative 1y equals 15

Line 2: Divide both sides of the equation by negative 1 so the equation is negative 1y over negative 1 equals 15 over negative 1.

Line 3: Simplify to get the solution y equals negative 15.

Line 4: Check your answer in the given equation negative y equals 15.

Line 4: Substitute y equals negative 15 into the equation, so it is negative 1 times negative 15 equals 15.

Line 5: Simplify to get 15 equals 15.

Since y equals negative 15 makes negative y equals 15 a true statement, negative 15 is the solution to the equation.

Solve 3 fourth times x equals 12, and verify the solution.

Line 1: Since the product of a number and its reciprocal is 1, we can multiply both sides of the equation by the reciprocal of 3 over 4 to eliminate the fraction, so the fraction is 4 over 3 times 3 over 4 times x equals 4 over 3 times 12.

Line 2: Multiply the reciprocals so the equation is 1x equals 4 over 3 times 12 over 1.

Line 3: Multiply the fractions to get the solution x equals 16

Line 4: Check your answer in the given equation 1 third times x equals 12.

Line 5: Substitute x equals 16 into the equation, so it is 1 third times 16 equals 12.

Line 6: Multiply the fractions so the equation is 1 over 3 times 16 over 1 equals 12.

Line 7: Simplify to get 12 equals 12.

Since x equals 16 makes 1 third times x equals 12 a true statement, 16 is the solution to the equation.

### Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.