1. Section 1.2 Linear Equations and Rational Equations

2. Solving Linear Equations in One Variable

6. Example
Solve and check:

7. Example
Solve and check:

8. Linear Equations with Fractions

10. Example
Solve and check:

11. Rational Equations

12. 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.

13. Example
Solve and check:

14. Types of Equations

15. 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

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

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

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