Exercise 3 Page 176

To solve the equation, we have to isolate g on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 92, the reciprocal of 29. This will eliminate the coefficient of 29g and isolate g.

2/9g=- 8

MultEqn

LHS * 9/2=RHS* 9/2

2/9g* 9/2=- 8* 9/2

▼

Simplify left-hand side

CommutativePropMult

Commutative Property of Multiplication

2/9* 9/2g=- 8* 9/2

MultFracByInverse

a/b* b/a=1

1g=- 8* 9/2

IdPropMult

Identity Property of Multiplication

g=- 8* 9/2

MoveLeftFacToNum

a*b/c= a* b/c

g=- 8* 9/2

Multiply

g=- 72/2

CalcQuot

Calculate quotient

g=- 36

To check that this solution is correct, let's substitute g=- 36 into the original equation and simplify.

2/9g=- 8

Substitute

g= - 36

2/9( - 36)? =- 8

MultPosNeg

a(- b)=- a * b

- 2/9(36)? =- 8

MoveRightFacToNum

a/c* b = a* b/c

- 2(36)/9? =- 8

Multiply

- 72/9? =- 8

CalcQuot

Calculate quotient

- 8=- 8 ✓

Since the left-hand side and right-hand side are equal, g=- 36 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.

Hints

Check the answer

Extra