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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 Transcript

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.

Summary and Worksheet

Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window