Exercise 43 Page 212

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a To solve an equation, using the Properties of Equality 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.

In this case, we need to start by removing the parentheses to simplify the left-hand side of the equation.

6 - (3 + x) = 10

Distr

Distribute $- 1$

6 - 3 - x = 10

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b To solve an equation, using the Properties of Equality 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.

In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

100 (x + 3) = 200

Distr

Distribute $100$

100 x + 300 = 200

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c To solve an equation, using the Properties of Equality 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.

In this case, we can start by multiplying the right- and left-hand side of the equation by

3

to remove the fraction.

\frac{1}{3} x + 4 = x - 2

MultEqn

$LHS \cdot 3 = RHS \cdot 3$

x + 12 = 3 x - 6

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d To solve an equation, using the Properties of Equality 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.

We can start by expanding the fraction

\frac{4}{5},

so it has the same denominator as

\frac{x + 2}{4 5} .

Then we will multiply both sides of the equation by

45

to remove the fractions.

\frac{4}{5} = \frac{x + 2}{4 5}

ExpandFrac

$\frac{a}{b} = \frac{a \cdot 9}{b \cdot 9}$

\frac{3 6}{4 5} = \frac{x + 2}{4 5}

MultEqn

$LHS \cdot 45 = RHS \cdot 45$

36 = x + 2

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Subchapter links

4.1.1 Line of Best Fit p.196-197

4.1.2 Residuals p.201-202

4.1.3 Upper and Lower Bounds p.205-206

4.1.4 Least Squares Regression Line p.210-213

Exercise 43 Page 212

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