determine whether each value of x is a solution of the inequality. (x+2)/(x-4) ≥3 (a) x=5 (b) x=

step 1 solution for the given question solution we have to check whether the given x values satisfies t

Determine whether each value of x is a solution of the...

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Key Concepts

Testing Candidate Solutions

Testing candidate solutions by substituting given values into the inequality is a method used to verify if those values satisfy the inequality. This approach involves replacing the variable with the specific candidate and checking whether the resulting expression holds true according to the inequality's direction and conditions. It also helps in confirming that the candidate values are within the valid domain of the rational expression.

Rational Inequalities

A rational inequality is an inequality that involves a rational expression (a fraction in which both the numerator and the denominator are polynomials). Solving such inequalities requires an understanding of how the signs of the numerator and the denominator contribute to the overall inequality. The process often involves determining the sign changes of the rational expression across its domain and finding the intervals where the inequality holds true.

Domain Restrictions

Domain restrictions are crucial when working with rational expressions because the denominator cannot be zero. Identifying values that make the denominator zero is important because these values are excluded from the solution set. In the context of rational inequalities, failing to consider domain restrictions may lead to including extraneous solutions that are not mathematically valid.

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