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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

3. Solving Equations Using Multiplication or Division

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Exercise 7 Page 261

Use the Multiplicative Inverse Property to isolate y.

y=9

Practice makes perfect

To solve the equation, we have to isolate y on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 32. Then, we will use the Multiplicative Inverse Property.

6=2y/3

LHS * 3/2=RHS* 3/2

3/2* 6=3/2* 2y/3

▼

Simplify right-hand side

MovePartNumRight

a* b/c=a/c* b

3/2* 6=3/2* 2/3* y

MultFracByInverse

a/b* b/a=1

3/2* 6=1* y

MoveRightFacToNum

a/c* b = a* b/c

3* 6/2=1* y

Multiply

18/2=y

Calculate quotient

9=y

Rearrange equation

y=9

To check that this solution is correct, let's substitute y=9 into the original equation and simplify.

6=2y/3

y= 9

6? =2( 9)/3

Multiply

6? =18/3

Calculate quotient

6=6 ✓

Since the left-hand side and right-hand side are equal, y=9 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.

Subchapter links

Try It p.260-261

Self-Assessment for Concepts & Skills p.261

Self-Assessment for Problem Solving p.262

Review & Refresh p.263

Concepts, Skills, & Problem Solving p.263-264