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Big Ideas Math: Modeling Real Life, Grade 7

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Big Ideas Math: Modeling Real Life, Grade 7 View details

Practice Test

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Exercise 4 Page 176

Use the Subtraction Property of Equality to eliminate the addition.

z=- 9.1

To solve the equation, we have to isolate z on one side. Using the Subtraction Property of Equality, we will subtract 14.5 from both sides of the equation. This will eliminate the addition. Let's do it!

z+14.5=5.4

LHS-14.5=RHS-14.5

z+14.5-14.5=5.4-14.5

Subtract term

z=- 9.1

To check that this solution is correct, let's substitute z=- 9.1 into the original equation and simplify.

z+14.5=5.4

z= - 9.1

- 9.1+14.5? =5.4

Add terms

5.4=5.4 ✓

Since the left-hand side and right-hand side are equal, z=- 9.1 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.