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Introduction to Solving Rational Inequalities
A rational inequality is an equation that states that two rational numbers are not equal. The inequality symbol is the less-than or equal-to sign (< or ≤), and it is placed between the two rational numbers.
To solve a rational inequality, you must first isolate the rational number on one side of the inequality symbol. You can then use the algebraic techniques that you know to solve the equation.
How to Solve Rational Inequalities
To solve rational inequalities, we use the same process as solving equations, but we also need to use the properties of inequalities.
To solve a rational inequality, we first isolate the rational expression on one side of the inequality symbol.
Next, we solve the rational expression for zero to find all the solutions to the inequality.
If the inequality is a strict inequality, we use the absolute value bars to make sure all the solutions are positive.
Finally, we graph the solutions on a number line.
Rationale
The rationale for this study is to investigate the effectiveness of a novel intervention, as compared to a control condition, on reducing symptoms of posttraumatic stress disorder (PTSD) in veterans. The study will also investigate the feasibility of the intervention. PTSD is a debilitating disorder that can significantly impair an individual’s quality of life. There is a need for effective interventions for PTSD that can be delivered in a variety of settings. The proposed intervention is a novel, self-administered, computer-based intervention that has the potential to be effective and feasible for a wide range of veterans.
Solved Example
The table below shows the average daily water requirement of a person.
Activity Average Daily Water Requirement Sleeping 8 cups Working 12 cups
A person usually drinks about four cups of water a day. How many cups of water does this person need to drink while working?
This person would need to drink about 16 cups of water while working.
