# Linear Equations in Disguise

Video solutions to help Grade 8 students learn how to solve equations that are not obviously linear equations.

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Lesson Plans and Worksheets for Grade 8

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New York State Common Core Math Module 4, Grade 8, Lesson 8
Lesson 8 Outcome

•Students rewrite and solve equations that are not obviously linear equations using properties of equality.

Lesson 8 Summary

•Proportions are linear equations in disguise and are solved the same way we normally solve proportions.
•When multiplying a fraction with more than one term in the numerator and/or denominator by a number, put the expressions with more than one term in parentheses so you remember to use the distributive property when transforming the equation.
NYS Math Module 4 Grade 8 Lesson 8 Classwork and Examples
Concept Development
Some linear equations may not look like linear equations upon first glance. A simple example that you should recognize is
x/5 = 6/12
What do we call this kind of problem and how do we solve it?

Theorem. Given rational numbers A, B, C, and D, so that B ≠ 0 and D ≠ 0, the property states
If A/B = C/D, then AD = BC.

Example 1 - Example 4: Given a linear equation in disguise, we will try to solve it.

Example 5: In the diagram below, △ABC ∼ △A'B'C'. Using what we know about similar triangles, we can determine the value of x.

Lesson 8 Exercises 1 - 4
Solve the following equations of rational expressions, if possible.

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