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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 1 Page 176

Use the Division Property of Equality to eliminate the multiplication.

x=- 37

To solve the equation, we have to isolate x on one side. Using the Division Property of Equality, we will divide both sides of the equation by 7. This will eliminate the multiplication and isolate x.

7x=- 3

.LHS /7.=.RHS /7.

7x/7=- 3/7

MovePartNumRight

a* b/c=a/c* b

7/7x=- 3/7

a/a=1

1x=- 3/7

Identity Property of Multiplication

x=- 3/7

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 3/7

To check that this solution is correct, let's substitute x=- 37 into the original equation and simplify.

7x=- 3

x= - 3/7

7( - 3/7)? =- 3

a(- b)=- a * b

- 7(3/7)? =- 3

DenomMultFracToNumber

7 * a/7= a

- 3 =- 3 ✓

Since the left-hand side and right-hand side are equal, x=- 37 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.