Exercise 19 Page 173

To solve the equation, we have to isolate w on one side. Using the Division Property of Equality, we will divide both sides of the equation by - 6.8. This will eliminate the multiplication and isolate w.

- 6.8w=3.4

DivEqn

.LHS /(- 6.8).=.RHS /(- 6.8).

- 6.8w/- 6.8=3.4/- 6.8

▼

Simplify

MovePartNumRight

a* b/c=a/c* b

- 6.8/- 6.8w=3.4/- 6.8

QuotOne

a/a=1

1w=3.4/- 6.8

IdPropMult

Identity Property of Multiplication

w=3.4/- 6.8

MoveNegNumToFrac

Put minus sign in front of fraction

w=-3.4/6.8

ReduceFrac

a/b=.a /3.4./.b /3.4.

w=- 1/2

WriteDec

Write as a decimal

w=- 0.5

To check that this solution is correct, let's substitute w=- 0.5 into the original equation and simplify.

- 6.8w=3.4

Substitute

w= - 0.5

- 6.8( - 0.5)? =3.4

MultNegNegOnePar

- a(- b)=a* b

6.8(0.5)? =3.4

Multiply

3.4=3.4 ✓

Since the left-hand side and right-hand side are equal, w=- 0.5 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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