§ 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4...

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§ 1.4 Solving Linear Equations

Transcript of § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4...

Page 1: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

§ 1.4

Solving Linear Equations

Page 2: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4

Linear Equations

Definition of a Linear Equation

A linear equation in one variable x is an equation that can be written in the form ax + b = 0, where a and b are real numbers and a is not equal to 0.

An example of a linear equation in x is 4x + 2 = 6. Linear equations in x are first degree equations in the variable x.

Page 3: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #3 Section 1.4

Properties of Equality

Property Definition

Addition Property of Equality

The same real number or algebraic expression may be added to both sides of an equation without changing the equation’s solution set.

Multiplication Property of Equality

The same nonzero real number may multiply both sides of an equation without changing the equation’s solution set.

Page 4: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #4 Section 1.4

Solving Linear Equations

Solving a Linear Equation

1) Simplify the algebraic expressions on each side.

2) Collect all the variable terms on one side and all the numbers, or constant terms, on the other side

3) Isolate the variable and solve.

4) Check the proposed solution in the original equation.

Page 5: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #5 Section 1.4

Solving Linear Equations

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Solve 4x + 2 = 10.

Page 6: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #6 Section 1.4

Solving Linear Equations

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Solve 6x -7 = 3x + 8.

Page 7: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #7 Section 1.4

Solving Linear Equations

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Solve: 5 - 3x + 4x = 1 - 7x + 12.

Page 8: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #8 Section 1.4

Categorizing an Equations

Type of Equations Definitions

Identity An equation that is true for all real numbers

Conditional An equation that is not an identity but is true for at least one real number

Inconsistent

(contradiction)

An equation that is not true for any real number

Page 9: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #9 Section 1.4

Categorizing an Equation

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation.

5 + 4x = 9x + 5

Page 10: § 1.4 Solving Linear Equations. Blitzer, Algebra for College Students, 6e – Slide #2 Section 1.4 Linear Equations Definition of a Linear Equation A linear.

Blitzer, Algebra for College Students, 6e – Slide #10 Section 1.4

Categorizing an Equation

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Solve and determine whether the equation is an identity, a conditional equation or an inconsistent equation.

5 – (2x – 4) = 2(x +1) - 4x


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2.4 – Writing Linear Equations. 2.4 – Writing Linear Equations Forms:

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