# Honors Geometry Companion Book, Volume 1

2.2.1 Algebraic Proof (continued)

The variable in this equation is n . In the original equation, 2 is added to 5 n . So, use the Subtraction Property of Equality and subtract 2 from both sides of the equation. After the equation is simplified, n is multiplied by 5. So, use the Division Property of Equality and divide both sides of the equation by 5. After the equation is simplified again, the result is − 2 = n . Since the variable n is isolated on one side of the equation, the equation is solved. However, the Symmetric Property of Equality can be applied to write the equation with n on the left side, as equations are more commonly written. The given equation in this example contains three variables, s , r , and p . Begin by using the Substitution Property of Equality to substitute given values for s and r . 54 is substituted into the equation for s because s is defined to be the speed of the object in km/h, and 54 km/h is the given speed of the object. The variable r is defined to be the scale of pixels per meter. So, since the given scale of pixels per meter is 8, 8 is substituted into the equation for r . After the substitution is complete and the equation is simplified by multiplying, the only operation that needs to be undone in the resulting equation is multiplication by 3.6. So, by the Division Property of Equality, both sides of the equation can be divided by 3.6. This operation isolates the variable p on one side of the equation, so the equation is solved.

Example 2 Technology Application

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