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ZingPath: Solving Linear Equations

Solving Two-Step Linear Equations

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Solving Linear Equations

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Solving Two-Step Linear Equations

Algebra-1

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You will determine the operations for solving two-step linear equations in one variable, create equations, and solve equations.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Solve two-step linear equations in one variable.

Everything You'll Have Covered

How to solve two-step linear equations in one variable

In this Activity Object, two-step linear equations in one variable are used. These are called two-step linear equations since they are solved with two inverse operations in the reverse order of operations. Remember, inverse operations are operations that undo each other. Addition and subtraction are inverse operations, as are multiplication and division. Another point to remember is that you need to perform the same operation on both sides of the equation to solve it. This is sometimes called balancing the equation so the equation is always equal.

In general, while solving a two-step linear equation in one variable:

1.    Note the operations performed on the variable in the equation.

2.    Apply the inverse operation to isolate the variable term (the variable and coefficient).

3.    Simplify the equation.

4.    Apply the inverse operation to isolate the variable.

5.    Simplify the equation.

You can check the answer by substituting the value for the variable in the original equation. The equation should be true. If not, your solution is false.

Let`s examine an equation: For the equation 6x + 3 = 24, there are two operations performed on x, multiplication and addition. To solve the equation, namely to find a number that makes the equation true, we need to apply inverse operation in the reverse order of the order of operations. For this example, we first need to do subtraction and then division.

6x + 3 = 24 Original equation.

6x + 3 - 3= 24 - 3 Subtract 3 from both sides.

6x = 21 Simplify.

Tutorial Details

Approximate Time 40 Minutes
Pre-requisite Concepts Learners should be familiar with equations, linear equations in one variable, reciprocal, solving one-step linear equations in one variable.
Course Algebra-1
Type of Tutorial Procedural Development
Key Vocabulary linear equations, linear equations in one variable, solution of the linear equation in one variable