Section 1.2 Linear Equations and Rational Equations

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Presentation transcript:

Section 1.2 Linear Equations and Rational Equations

Solving Linear Equations in One Variable

Example Solve and check:

Example Solve and check:

Linear Equations with Fractions

Example Solve and check:

Rational Equations

A rational equation is an equation containing one or more rational expressions. In the previous example we saw a rational equation with constants in the denominators. That rational equation was a linear equation. The rational equation below is not a linear equation. The solution procedure still involves multiplying each side by the least common denominator. We must avoid any values of the variable that make a denominator zero.

Example Solve and check:

Types of Equations

An equation that is true for all real numbers for which both sides are defined is called an identity. An example of an identity is X+3=X+2+1 An equation that is not an identity, but that is true for at least one real number, is called a conditional equation. 2X=8 An inconsistent equation is an equation that is not true for even one real number. An example of an inconsistent equation is X=X+7

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

Solve and check: (a) (b) (c) (d)

Solve the equation. (a) (b) (c) (d)