Solving Linear Equations Algebraically

Solving Multi-Step Equations - Part 1

Get ready to apply the properties of real numbers and the properties of equality to solve multi-step linear equations, in one variable. Your knowledge of inverse operations will be beneficial as you work through this interactivity. Click the player button to begin.

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Solving Multi-Step Equations - Part 2

Continue applying your skills solving equations as you solve multi-step equations that include variables on both sides. Your knowledge of the properties of real numbers, the properties of equality, and inverse operations will continue to serve as an excellent resource to you. Click the player button to begin.

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Using Cross-Multiplication to Solve Equations

When each side of an equation consists of a fraction, as in the example shown below, you can eliminate the fractions by cross-multiplying. To cross-multiply, find the product of the denominator on each side and the numerator of the opposite side. The products are equal.

5x − 4/3 = 7x/2

2(5x − 4) = 3 · 7x

Apply the distributive property to the left side of the equation and find the product of the terms on the right side of the equation.

Then, begin using inverse operations to isolate the variable. Subtract 10x from both sides of the equation.

Divide each term by 11.

 

Determining the Number of Solutions

A linear equation may have one solution, no solutions, or an infinite number of solutions. You are most likely familiar with solving an equation that has only one solution. For example, the equation in the example above has one solution, −20/11. Take a look at the following examples so that you will be able to determine when an equation has no solutions or an infinite number of solutions.

• If the result is an invalid statement, the equation has no solutions.

−1 = 4 is invalid. Therefore, the equation 5x − 1 = 4 + 5x has no solutions.

• If the result is identical and equivalent expressions, the equation has an infinite number of solutions.

7x − 4 = 4x − 4 + 3x

7x − 4 = 7x − 4

The result is identical and equivalent expressions. Any value substituted for x will make the equation true. Therefore, the equation has an infinite number of solutions.

 

Solving Equations Using Algebra Tiles

Algebra tiles can be used to model the steps to solving equations. In this interactivity, you will learn how to use algebra tiles to model and solve multi-step linear equations. Click the player button to begin.

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Solving Linear Equations Algebraically Review

Now that you have learned about solving linear equations algebraically, review your knowledge in this interactivity. Click the player button to get started.

 

 

 

Did you answer the content review incorrectly? Do you want more instruction or extra practice? If so, view the video Solving Multi-Step Linear Equations Algebraically from eMediaVASM.