3.1.3 Solving Inequalities by Multiplying or Dividing (continued) Example 2 Using Multiplication and Division by a Negative Number to Solve Inequalities The process used to solve an inequality is very similar to the process used to solve an equation. In both cases, inverse operations are used to isolate the variable. However, the process for solving inequalities has an additional step when the inequality is multiplied or divided by a negative number. Consider the inequality 1 < 2, which is a true statement. If both sides of the inequality are multiplied by − 3, then the result is − 3 < − 6, which is no longer a true statement. However, if both sides are multiplied by − 3 and the direction of the inequality symbol is reversed (from < to > ), the result is − 3 > − 6, which is a true statement. So, if an inequality is multiplied (or divided) by a negative number, the direction of the inequality symbol must be reversed in order for the statement to remain true. Use this fact when solving inequalities. To solve an inequality where the variable is • multiplied by a negative number, divide both sides by that coefficient and reverse the inequality symbol. • divided by a negative number, multiply both sides by that number and reverse the inequality symbol.
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