Solve the compound inequality. Write the answer in interval...

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Key Concepts

Compound Inequalities

Compound inequalities involve two or more individual inequalities that are connected by logical operators such as 'and' or 'or'. They require solving each inequality separately and then combining the solutions appropriately (using union for 'or' conditions and intersection for 'and' conditions) to find the overall solution set.

Rational Inequalities

Rational inequalities include expressions represented as ratios of polynomials. Solving them often involves clearing denominators by multiplying both sides by a common denominator, with the crucial emphasis on considering the sign of the denominator to ensure that the direction of the inequality is maintained correctly.

Inequality Manipulation Rules

Inequality manipulation rules involve performing operations such as addition, subtraction, multiplication, or division on both sides of an inequality while preserving its order. Special caution is required when multiplying or dividing by negative values, as these operations necessitate reversing the inequality sign.

Interval Notation

Interval notation is a system for writing subsets of the real numbers in a compact form. It uses brackets to denote inclusion of endpoints and parentheses to denote exclusion, effectively representing continuous ranges of numbers that form the solution set to an inequality.

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