Linear Equations - 1

Linear Equations - 1

 To solve equations for the unknown, use inverse operations to isolate the variable. These inverse operations ‘‘undo’’ what has been done to the variable. That is, inverse operations are used to move quantities across the equal sign. For instance, in the equation 5x = 10, x is multiplied by 5, so to move 5 across the equal sign, you need to ‘‘unmultiply’’ the 5. That is, divide both sides of the equation by 5 (equivalently, multiply each side of the equation by ¹/₅). In the equation 5 + x = 10, to move 5 across the equal sign, you must ‘‘unadd’’ 5. That is, subtract 5 from both sides of the equation (equivalently, add –5 to both sides of the equation).

Linear Equations

Linear Equations

Linear Equations

Now we can use the tools we have developed to solve equations. Up to now, we have rewritten expressions and added fractions. This chapter is mostly concerned with linear equations. In a linear equation, the variables are raised to the first power—there are no variables in denominators, no variables to any power (other than one), and no variables under root signs.

Factoring To Reduc Fractions - 2

Factoring To Reduc Fractions - 2

Once the LCD is found rewrite each fraction in terms of the LCD—multiply each fraction by the ‘‘missing’’ factors over themselves. Then add or subtract the numerators.

Factoring To Reduc Fractions - 1

Factoring To Reduc Fractions - 1

            Before adding or subtracting fractions factor the denominator. Once the denominator is factored you can determine the LCD.

Factoring To Reduce Fractions

Factoring To Reduce Fractions

Factoring To Reduce Fractions

To reduce a fraction to its lowest terms, factor the numerator and denominator. Cancel any like factors.