Exercise 57 Page 87

Every equation has an

equals

sign

and values or expressions on either of its sides. Key phrases such as

is,

is equal to,

and

equals

tell us about the placement of the equals sign.

two thirds = negative eight times a number

On the right-hand side we have one key word, which is times. This word tells us the operation that will be used in our equation. Times indicates multiplication.

Negative eight times a number - 8 \times x ⇕ - 8 x

By connecting the left-hand side and the right-hand side with an equals sign, we have a complete equation.

\frac{2}{3} = - 8 x

Finally, we can solve the equation we have written. We will do this using inverse operations and following the Properties of Equality.

\frac{2}{3} = - 8 x

MultEqn

$LHS \cdot (- \frac{1}{8}) = RHS \cdot (- \frac{1}{8})$

\frac{2}{3} (- \frac{1}{8}) = - 8 x (- \frac{1}{8})

MultPosNeg

$a (- b) = - a \cdot b$

- \frac{2}{3} (\frac{1}{8}) = - 8 x (- \frac{1}{8})

MultFrac

Multiply fractions

- \frac{2}{2 4} = - 8 x (- \frac{1}{8})

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

- \frac{1}{1 2} = - 8 x (- \frac{1}{8})

CommutativePropMult

Commutative Property of Multiplication

- \frac{1}{1 2} = x (- 8) (- \frac{1}{8})

MultNegNegOnePar

$- a (- b) = a \cdot b$

- \frac{1}{1 2} = x (8) (\frac{1}{8})

DenomMultFracToNumber

$8 \cdot \frac{a}{8} = a$

- \frac{1}{1 2} = x (1)

IdPropMult

Identity Property of Multiplication

- \frac{1}{1 2} = x

RearrangeEqn

Rearrange equation

x = - \frac{1}{1 2}