Exercise 109 Page 479

Practice makes perfect

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

24 = 3 x + 3

SubEqn

$LHS - 3 = RHS - 3$

24 - 3 = 3 x + 3 - 3

SubTerm

Subtract term

21 = 3 x

RearrangeEqn

Rearrange equation

3 x = 21

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

6 x + 12 = - x - 2

AddEqn

$LHS + x = RHS + x$

6 x + 12 + x = - x - 2 + x

CommutativePropAdd

Commutative Property of Addition

6 x + x + 12 = - x + x - 2

AddTerms

Add terms

7 x + 12 = - 2

SubEqn

$LHS - 12 = RHS - 12$

7 x + 12 - 12 = - 2 - 12

SubTerm

Subtract term

7 x = - 14

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A shortcut to better grades

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To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side 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.