Exercise 42 Page 10

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, the variable term is already on the right-hand side of the equation, so we will start by simplifying the constants in the equation.

8/9=x+1/3(7)

MoveRightFacToNumOne

1/b* a = a/b

8/9=x+7/3

SubEqn

LHS-7/3=RHS-7/3

8/9-7/3=x+7/3-7/3

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Simplify denominator

ExpandFrac

a/b=a * 3/b * 3

8/9-7* 3/3* 3=x+7/3-7/3

Multiply

Multiply

8/9-21/9=x+7/3-7/3

SubFrac

Subtract fractions

- 13/9=x

FracToMixed

Write fraction as a mixed number

- 1 49=x

RearrangeEqn

Rearrange equation

x=- 1 49

The solution to the equation is x= - 1 49. We can check our solution by substituting it into the original equation.

8/9=x+1/3(7)

Substitute

x= - 1 49

8/9? = - 1 49+1/3(7)

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Simplify

MixedToFrac

a bc=a* c+b/c

8/9? =- 1* 9+4/9+1/3(7)

IdPropMult

Identity Property of Multiplication

8/9? =- 9+4/9+1/3(7)

AddTerms

Add terms

8/9? =- 13/9+1/3(7)

MoveRightFacToNumOne

1/b* a = a/b

8/9? =- 13/9+7/3

ExpandFrac

a/b=a * 3/b * 3

8/9? =- 13/9+7* 3/3* 3

Multiply

Multiply

8/9? =- 13/9+21/9

AddFrac

Add fractions

8/9=8/9 ✓

Since the left-hand side is equal to the right-hand side, our solution is correct.