Exercise 22 Page 375

Practice makes perfect

a To solve an equation using the Properties of Equality, we should first gather all variables on one side of the equation and all constants on the other side. We can start by expanding fractions so they have the same denominator, then multiply both sides of the equation by this denominator to remove the fractions.

4x/5=x-2/7

ExpandFrac

a/b=a * 7/b * 7

28x/35=x-2/7

ExpandFrac

a/b=a * 5/b * 5

28x/35=5(x-2)/35

Distr

Distribute 5

28x/35=5x-10/35

MultEqn

LHS * 35=RHS* 35

28x=5x-10

Now we can continue to solve using the Properties of Equality.

28x=5x-10

SubEqn

LHS-5x=RHS-5x

23x=- 10

DivEqn

.LHS /23.=.RHS /23.

x=- 10/23

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 10/23

The solution to the equation is x=- 1023.

b To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side by using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

- 3(2b-7)=- 3b+21-3b

Distr

Distribute - 3

- 6b +21=- 3b+21-3b

Now we can continue to solve using the Properties of Equality.

- 6b +21=- 3b+21-3b

SubTerm

Subtract term

- 6b +21=- 6b+21

AddEqn

LHS+6b=RHS+6b

21=21

Simplifying the equation resulted in an identity. Thus, the equation has infinitely many solutions.

c To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side by using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

6-2(c-3)=12

Distr

Distribute - 2

6-2c+6=12

Now we can continue to solve using the Properties of Equality.

6-2c+6=12

AddTerms

Add terms

- 2c+12=12

SubEqn

LHS-12=RHS-12

- 2c=0