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Core Connections Algebra 1, 2013

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Core Connections Algebra 1, 2013 View details

2. Section 6.2

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Exercise 104 Page 291

Practice makes perfect

a Although it may look complicated, notice that this is an application of the Distributive Property.

2x(x+3)

Distribute 2x

2x(x)+2x(3)

Multiply

2x^2+6x

b We want to simplify the expression by multiplying the binomials. To do so we will apply the Distributive Property.

(3x+2)(x-3)

Distribute (x-3)

3x(x-3)+2(x-3)

Distribute 3x

3x^2-9x+2(x-3)

Distribute 2

3x^2-9x+2x-6

Add terms

3x^2-7x-6

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.

4y-2(6-y)=6

Distribute - 2

4y-12+2y=6

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

4y-12+2y=6

Add terms

6y-12=6

LHS+12=RHS+12

6y=18

.LHS /6.=.RHS /6.

y=3

The solution to the equation is y=3.

d 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- and right-hand sides of the equation.

x(2x-4)=(2x+1)(x-2)

Distribute x

2x^2-4x=(2x+1)(x-2)

Distribute (x-2)

2x^2-4x=2x(x-2)+1(x-2)

Distribute 2x

2x^2-4x=2x^2-4x+1(x-2)

Identity Property of Multiplication

2x^2-4x=2x^2-4x+x-2

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

2x^2-4x=2x^2-4x+x-2

LHS-2x^2=RHS-2x^2

- 4x=- 4x+x-2

Add terms

- 4x=- 3x-2

LHS+3x=RHS+3x

- x=- 2

LHS * (- 1)=RHS* (- 1)

x=2

The solution to the equation is x=2.

Subchapter links

6.2.1 Residual Plots p.271-273

6.2.2 Correlation p.279-280

6.2.3 Association is Not Causation p.283-285

6.2.4 Interpreting Correlation in Context p.290-291

6.2.5 Curved Best-Fit Models p.296-298