1. solving equations the addition principle

OBJECTIVES

1.1 Solving Equations: The Addition Principle

dUse < or > for to

write a true statement in a situation like 6 10.

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a Determine whether a given number is a solution of agiven equation.

b Solve equations using the addition principle.

1.1 Solving Equations: The Addition Principle

aDetermine

whether a given number is a solution of a

given equation.

EQUATION

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

An equation is a number sentence that says that the expressions on either side of the equals sign, =, represent the same number.

EXAMPLE

1.1 Solving Equations: The Addition Principle

aDetermine whether a given number is a solution of agiven equation.

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Determine whether each equation is true, false, or neither.

1.1 Solving Equations: The Addition Principle

aDetermine

whether a given number is a solution of a

given equation.

SOLUTION OF AN EQUATION

Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Any replacement for the variable that makes an equation true is called a solution of the equation. To solve an equation means to find all of its solutions.

EXAMPLE

1.1 Solving Equations: The Addition Principle

aDetermine whether a given number is a solution of agiven equation.

Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Since the left-hand and the right-hand sides are not the same, 19 is not a solution of the equation.

Determine whether 19 is a solution of 7x = 141.

1.1 Solving Equations: The Addition Principle

bSolve equations using the addition principle.

EQUIVALENT EQUATIONS

Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Equations with the same solutions are called equivalent equations.

1.1 Solving Equations: The Addition Principle

bSolve equations using the addition principle.

THE ADDITION PRINCIPLE FOR EQUATIONS

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EXAMPLE

1.1 Solving Equations: The Addition Principle

b Solve equations using the addition principle.

Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

1.1 Solving Equations: The Addition Principle

b Solve equations using the addition principle.

Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

1.1 Solving Equations: The Addition Principle

b Solve equations using the addition principle.

7

Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

1.1 Solving Equations: The Addition Principle

b Solve equations using the addition principle.

7

Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.