Nursing Entrance Exam

Nursing Preparation Study Guide

3.5.5 Solving Inequalities While solving inequalities, we need to apply the same rules of operations (addition, subtraction, multiplication, and division). As with equations, whatever is done to one side must be done to the other side. However, there is one additional rule: If multiplying or dividing by a negative number, reverse the sign of inequality. For instance: − } ≤ 10 , multiplying both sides by −3 will become, D − } × −3 ≥ 10 × −3 D It should be noted that in this case, the sign of inequality has been reversed from ‘less than or equal to’ to ‘greater than or equal to’. Now, let us practice some examples to solve the inequalities. Inequalities Solution + ( + 2) < 16 Step 1: Simplify the inequality + + 2 < 16 2 + 2 < 16 Step 2: Subtract 2 from both sides 2 + 2 − 2 < 16 − 2 2 < 14 Step 3: Divide both sides by 2 2 2 < 14 2 Answer: < 5 ≤ 25 Step 1: Divide both sides by 5 5 5 ≤ 25 5 Answer: ≤ − 5 ≥ 17 Step 1: Add 5 to both sides − 5 + 5 ≥ 17 + 5 Answer: ≥ − 2 + 10 < 64 Step 1: Subtract 10 from both sides − 2 + 10 − 10 < 64 − 10 −2 < 54 Step 2: Divide both sides by (−2) & reverse the inequality sign − 2 −2 < 54 −2 Answer: > −

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