1.10 Solving Equations

  • Types of Equations • Solving Basic Types of Equations • Checking the Solution • First Steps • Ratio and Proportion

In this section, we show how algebraic operations are used in solving equations. In the following sections, we show some of the important applications of equations.

An equation is an algebraic statement that two algebraic expressions are equal. Any value of the unknown that produces equality when substituted in the equation is said to satisfy the equation and is called a solution of the equation.

EXAMPLE 1 Valid values for equations

The equation 3x − 5 = x + 1 is true only if x = 3. Substituting 3 for x in the equation, we have 3(3) − 5 = 3 + 1 ,  or 4 = 4 ;  substituting x = 2 ,  we have 1 = 3 ,  which ...

Get Basic Technical Mathematics, 11th Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.