Exercise 92 Page 83

a To evaluate the expression, we have to substitute

x = - 2,

y = - 3,

and

z = 5

into the expression and follow the order of operations to simplify.

2 x + 3 y + z

SubstituteValues

Substitute values

2 (- 2) + 3 (- 3) + 5

MultPosNeg

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

- 4 - 9 + 5

AddSubTerms

Add and subtract terms

- 8

b Like in Part A, we have to substitute

x = - 2

and

y = - 3

into the expression and follow the order of operations to simplify.

x - y

SubstituteII

$x = - 2$ , $y = - 3$

- 2 - (- 3)

SubNeg

$a - (- b) = a + b$

- 2 + 3

AddTerms

Add terms

1

c Like in Parts A and B, we have to substitute

x = - 2,

y = - 3

and

z = 5

into the expression and follow the order of operations to simplify.

2 (\frac{x + y}{z})

SubstituteValues

Substitute values

2 (\frac{- 2 + ( - 3 )}{5})

AddNeg

$a + (- b) = a - b$

2 (\frac{- 2 - 3}{5})

SubTerm

Subtract term

2 (\frac{- 5}{5})

MoveNegNumToFrac

Put minus sign in front of fraction

2 (- \frac{5}{5})

QuotOne

$\frac{a}{a} = 1$

2 (- 1)

MultPosNeg

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

- 2

d Like in previous parts, we have to substitute

x = - 2

into the expression and follow the order of operations to simplify.

3 x^{2} - 2 x + 1

Substitute

$x = - 2$

3 (- 2)^{2} - 2 (- 2) + 1

NegBaseToPosBase

$(- a)^{2} = a^{2}$

3 (4) - 2 (- 2) + 1

MultNegNegOnePar

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

3 (4) + 2 (2) + 1

Multiply

12 + 4 + 1

AddTerms

Add terms

17

e Like in previous parts, we have to substitute

x = - 2,

and

y = - 3

into the expression and follow the order of operations to simplify.

3 y (x + x^{2} - y)

SubstituteII

$x = - 2$ , $y = - 3$

3 (- 3) (- 2 + (- 2)^{2} - (- 3))

NegBaseToPosBase

$(- a)^{2} = a^{2}$

3 (- 3) (- 2 + 4 - (- 3))

SubNeg

$a - (- b) = a + b$

3 (- 3) (- 2 + 4 + 3)

AddTerms

Add terms

3 (- 3) (5)

MultPosNeg

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

- 3 (3) (5)

Multiply

- 45

f Like in previous parts, we have to substitute

x = - 2,

y = - 3,

and

z = 5

into the expression and follow the order of operations to simplify.

\frac{- z ^{2} ( 1 - 2 x )}{y - x}

SubstituteValues

Substitute values

\frac{- 5 ^{2} ( 1 - 2 ( - 2 ) )}{- 3 - ( - 2 )}

MultPosNeg

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

\frac{- 5 ^{2} ( 1 + 4 )}{- 3 - ( - 2 )}

SubNeg

$a - (- b) = a + b$

\frac{- 5 ^{2} ( 1 + 4 )}{- 3 + 2}

AddTerms

Add terms

\frac{- 5 ^{2} ( 5 )}{- 1}

CalcPow

Calculate power

\frac{- 2 5 ( 5 )}{- 1}

Multiply

\frac{- 1 2 5}{- 1}

DivNegNeg

$\frac{- a}{- b} = \frac{a}{b}$

\frac{1 2 5}{1}

DivByOne

$\frac{a}{1} = a$

125

Subchapter links

2.3.1 Finding an Equation Given the Slope and a Point p.80

2.3.2 Finding the Equation of a Line Through Two Points p.82-83

Extension Activity Finding y=mx+b from Graphs and Tables p.85

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