Exercise 29 Page 143

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 only variable term is already on the left-hand side of the equation, so we will start by subtracting 2 from both sides. Now, we are going to multiply the equation by - 3 using the Multiplication Property of Equality to eliminate the fraction. Let's go!

- b/3=- 9/2

MoveNegFracToDenom

Put minus sign in denominator

b/- 3=- 9/2

MultEqn

LHS * (- 3)=RHS* (- 3)

b/- 3 * (- 3) =- 9/2 * (- 3)

FracMultDenomToNumber

a/(- 3)* (- 3) = a

b =- 9/2 * (- 3)

MoveRightFacToNum

a/c* b = a* b/c

b =- 9(- 3)/2

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Multiply

MultNegNegOnePar

- a(- b)=a* b

b =9 * 3/2

Multiply

Multiply

b =27/2

FracToMixed

Write fraction as a mixed number

b = 13 12

The solution to the equation is b = 13 12. We can check our solution by substituting it into the original equation.

2-b/3=- 5/2

Substitute

b= 13 12

2-13 12/3 ? = - 5/2

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Simplify

MixedToFrac

a bc=a* c+b/c

2-13 * 2 + 12/3 ? = - 5/2

Multiply

Multiply

2-26 + 12/3 ? = - 5/2

AddTerms

Add terms

2-272/3 ? = - 5/2

DivFracD

a/c/b= a/b* c

2-27/3 * 2 ? = - 5/2

Multiply

Multiply

2-27/6 ? = - 5/2

Rewrite

Rewrite 2 as 12/6

12/6-27/6 ? = - 5/2

SubFrac

Subtract fractions

12-27/6 ? = - 5/2

SubTerm

Subtract term

- 15/6 ? = - 5/2

ReduceFrac

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

- 15/3/6/3 ? = - 5/2

CalcQuot

Calculate quotient

- 5/2 ? = - 5/2

MoveNegNumToFrac

Put minus sign in front of fraction

- 5/2=- 5/2

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