3.2.2 Solving Inequalities with Variables on Both Sides

Key Objectives • Write and solve inequalities with variable terms on both sides. • Solve inequalities that are identities or contradictions. Key Terms • An identity is an equation or inequality that is true for all values of the variable. The equation or inequal- ity is always true. • A contradiction is an equation or inequality that has no solutions. The equation or inequality is never true. Some inequalities have variable terms on both sides of the inequality symbol. To solve these inequalities, use the same process as for solving equations with variable terms on both sides, but remember to reverse the inequality symbol if both sides of the inequality are multiplied or divided by a negative number. Example 1 Solving Inequalities with Variables on Both Sides As with equations with variable terms on both sides, begin solving an inequality with variable terms on both sides by collecting those variable terms on either side of the inequality.

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