Exercise 6 Page 173

To solve the equation, we have to isolate v on one side. Using the Addition Property of Equality, we will add 5/6 to both sides of the equation. This will eliminate the subtraction. Let's do it!

v-5/6=- 7/8

AddEqn

LHS+5/6=RHS+5/6

v-5/6+5/6=- 7/8+5/6

AddTerms

Add terms

v=- 7/8+5/6

▼

Simplify

ExpandFrac

a/b=a * 3/b * 3

v=- 7* 3/8* 3+5/6

Multiply

v=- 21/24+5/6

ExpandFrac

a/b=a * 4/b * 4

v=- 21/24+5* 4/6* 4

Multiply

v=- 21/24+20/24

MoveNegFracToNum

Put minus sign in numerator

v=- 21/24+20/24

AddFrac

Add fractions

v=- 21+20/24

AddTerms

Add terms

v=- 1/24

MoveNegNumToFrac

Put minus sign in front of fraction

v=- 1/24

To check that this solution is correct, let's substitute v=- 124 into the original equation and simplify.

v-5/6=- 7/8

Substitute

v= - 1/24

- 1/24-5/6? =- 7/8

▼

Simplify

ExpandFrac

a/b=a * 4/b * 4

- 1/24-5* 4/6* 4? =- 7/8

Multiply

- 1/24-20/24? =- 7/8

MoveNegFracToNum

Put minus sign in numerator

- 1/24-20/24? =- 7/8

SubFrac

Subtract fractions

- 1-20/24? =- 7/8

SubTerm

Subtract term

- 21/24? =- 7/8

ReduceFrac

a/b=.a /3./.b /3.

- 7/8? =- 7/8

MoveNegNumToFrac

Put minus sign in front of fraction

- 7/8=- 7/8 ✓

Since the left-hand side and right-hand side are equal, v=- 124 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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