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pg 317 #'s 3, 4, 5, 6, 11
6.1 Solving Inequalities by Addition and Subtraction
To solve an equation, isolate the variable. An inequality of Addition property and Subtraction property is solved the same way.
In linear inequalities, there are infinitely many solutions to an inequality. The solution to inequalities can be written in set builder notation, for example
{x l x > 3}. This is read as the set of all numbers x such that x is greater than 3.
The number found when solving an inequality is a boundary that is sometimes included in the solution and sometimes not. It is included in the solutions if the inequality sign is , but it is not included if the symbol is <>.
If the boundary number is included, a solid dot is placed at that point on the number line. If the number is not included, use an open circle. Then draw an arrow to the right if the rest of the solution set is greater than the boundary or to the left if the rest of the solution set is less than the boundary.
6.1 Solving Inequalities by Multiplication and Division
Inequalities that include multiplication or division of the variable can also be solved. The same principles as found in the Multiplication and Division Properties of Equality are used, with one main difference.
If an inequality is multiplied or divided by the same negative number on each side, then inequality symbol is reversed. The symbol must be reversed to result in a true inequality. The inequality sign is not reversed if each side is multiplied of divided by the same positive number.
