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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

4. Congruence and Transformations

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Exercise 42 Page 206

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

- 2 (8 - y) = - 6 y

Note that, instead of distributing, we can divide both sides of the equation by

- 2,

using the Division Property of Equality.

- 2 (8 - y) = - 6 y

$LHS / (- 2) = RHS / (- 2)$

\frac{- 2 ( 8 - y )}{- 2} = \frac{- 6 y}{- 2}

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

\frac{2 ( 8 - y )}{2} = 3 y

CancelCommonFac

Cancel out common factors

8 - y = 3 y

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

8 - y = 3 y

$LHS + y = RHS + y$

8 - y + y = 3 y + y

Add terms

8 = 4 y

$LHS / 4 = RHS / 4$

\frac{8}{4} = \frac{4 y}{4}

Calculate quotient

2 = y

Rearrange equation

y = 2

The solution to the equation is

y = 2 .

We can check our solution by substituting it into the original equation.

- 2 (8 - y) = - 6 y

$y = 2$

- 2 (8 - 2) = ? - 6 (2)

▼

Simplify

Subtract term

- 2 (6) = ? - 6 (2)

Multiply

- 12 = - 12

Since the left-hand side is equal to the right-hand side, our solution is correct.

Subchapter links

Communicate Your Answer p.199

Monitoring Progress p.200-203