Exercise 29 Page 263

To solve the equation, we have to isolate m on one side. Using the Division Property of Equality, we will divide both sides of the equation by 4. This will eliminate the multiplication and isolate m.

3/5=4m

DivEqn

.LHS /4.=.RHS /4.

3/5÷ 4=4m÷ 4

WriteAsFrac

Write as a fraction

3/5÷ 4/1=4m÷ 4/1

DivFracByFracDiv

a/b÷c/d=a/b*d/c

3/5* 1/4=4m* 1/4

CommutativePropMult

Commutative Property of Multiplication

3/5* 1/4=m* 4* 1/4

WriteAsFrac

Write as a fraction

3/5* 1/4=m* 4/1* 1/4

MultFrac

Multiply fractions

3* 1/5* 4=m* 4* 1/1* 4

Multiply

3/20=m* 4/4

CalcQuot

Calculate quotient

3/20=m*1

IdPropMult

Identity Property of Multiplication

3/20=m

RearrangeEqn

Rearrange equation

m=3/20

To check that this solution is correct, let's substitute m= 320 into the original equation and simplify.

3/5=4m

Substitute

m= 3/20

3/5? =4( 3/20)

MoveRightFacToNum

a/c* b = a* b/c

3/5? =4* 3/20

Multiply

3/5? =12/20

ReduceFrac

a/b=.a /4./.b /4.

3/5? =12÷ 4/20÷ 4

SimpQuot

Simplify quotient

3/5=3/5 ✓

Since the left-hand side and right-hand side are equal, m= 320 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.

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