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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 18 Page 263

Use the Multiplication Property of Equality to eliminate the division.

x=24

Practice makes perfect

To solve the equation, we have to isolate x on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 6. This will eliminate the denominator of the fraction and isolate 5x.

5x÷ 6=20

a÷ b=a/b

5x/6=20

LHS * 6=RHS* 6

5x/6* 6=20* 6

FracMultDenomToNumber

a/6* 6 = a

5x=20* 6

Multiply

5x=120

.LHS /5.=.RHS /5.

5x/5=120/5

MovePartNumRight

a* b/c=a/c* b

5/5* x=120/5

Calculate quotient

1* x =24

Identity Property of Multiplication

x=24

To check that this solution is correct, let's substitute x=24 into the original equation and simplify.

5x÷ 6=20

x= 24

5( 24)? =120

Multiply

120=120 ✓

Since the left-hand side and right-hand side are equal, x=24 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