Problems 80-83 are based on material learned earlier in the...

Problems $80-83$ are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Solve: $\frac{3}{x-2} \geq 5$

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Key Concepts

Sign Analysis

Sign analysis involves testing the sign of the rational expression in each interval determined by the critical points. By substituting test values from each interval into the expression, one can determine whether the result is positive or negative, which allows for the identification of intervals that satisfy the inequality.

Critical Points Identification

Critical points are the values of the variable that either make the numerator equal to zero or cause the expression to be undefined due to the denominator equaling zero. These points divide the number line into intervals over which the sign of the expression can be analyzed.

Rational Inequalities

Rational inequalities are inequalities that involve rational expressions, which are ratios of polynomials. Solving these inequalities requires determining the values of the variable that make the inequality true, while taking into account any restrictions in the domain of the expression.

Domain Restrictions

Before solving a rational inequality, it is important to identify the domain of the rational expression, which consists of all values for which the denominator is not zero. Any value that makes the denominator zero is excluded from the solution because it results in an undefined expression.

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