Inequalities (GMAT Focus Edition – Quantitative Reasoning Content and Tactics)

AnalystPrep's GMAT® Focus Course Can Be Found Here: https://analystprep.com/shop/gmat-focus-complete-course-offered-by-analystprep/

Book a One-on-One Tutoring Session with Stefan Here: https://analystprep.com/shop/1-on-1-online-tutoring-by-myguru-and-analystprep/

Inequalities Defined
- Indicate Values that are Greater or Lesser Than Another Value
- Open End of Inequality Sign Faces Larger Value | ie. 5 larger than 3
- Used to Relate Known Values or Variables
- Can be Algebraically Manipulated or Combined in a Similar Manner
as Equations if All Values or Variables in Inequality are Known to be larger than 0
- If Multiplying or Dividing Inequality by Value less than 0 🡪 Must Flip Inequality

Strategic Implications
- If All Values for Inequality Problem Defined as larger than 0
🡪 Prepare to Manipulate Algebraically
- Recognize that Inequalities are Not Same as Equations in Considering Sufficiency
- For Complex Inequalities Consider Alternative Tactics 🡪 Especially Modeling & Logical Evaluation

Algebraic Order of Operations
- First 🡪 Eliminate Fractions or Decimals by Multiplying Full Inequalityby Least Common Denominator or Power of 10
- Then 🡪 Work to Efficiently Simplify Inequality Using Four Basic Functions Following PEMDAS Order, Avoiding Negatives as Possible
- Last 🡪 Eliminate Exponents or Radicals by Appropriately Raising or Rooting Full Equation Remembering to Account for Negative if Needed

Solving Inequalities Involving Negatives
- First 🡪 Manipulate as Much as Possible without Multiplying or Dividing by a Value less than 0 & Remember Possible to Add or Subtract Inequalities by Value less than 0 Without Flipping Inequality Sign
- Last 🡪 Multiply or Divide Inequality by Value less than 0 and Flip Inequality Sign
- Time Permitting 🡪 Check Solution Against Original Equation to Confirm

Solving Compound Inequalities
- First 🡪 Split Single Compound Inequality Into as Many Separate Inequalities as Necessary | One for Each Inequality Sign
- Next 🡪 Seek to Isolate for Sought Value in Each Inequality
- Last 🡪 Recombine Compound Inequality if Helpful in Solving Problem or Evaluating Data Sufficiency

Systems of Inequalities
- Used to Evaluate Individual Variables or Combinations of Variables Involving Multiple Inequalities Pending Direction of Inequality Signs
- Two Inequalities with Sign Facing Same Direction Can be Accurately Combined Through Addition Without Any Change to Direction
- Two Inequalities with Signs in Opposite Directions Can be Accurately Combined Through Subtraction Taking Direction of First Inequality

Strategic Implications
- Only Attempt to Combine Systems of Inequalitiesif Certain of Steps to Complete Combination
- Seek Methods of Manipulation to FacilitateAddition of Two Inequalities
- Be Careful When Combining Through Subtraction

Adding a System of Inequalities
- First 🡪 Stack Equations Vertically Aligning Variables and EnsureSame Direction for Signs
- Then 🡪 Carefully Add Inequalities Keeping Sign Facing Same Direction
- Last 🡪 Simplify Following Rules of Inequality Manipulation

Subtracting a System of Inequalities
- First 🡪 Stack Equations Vertically Aligning Variables and Ensure Opposing Directions for Signs
- Then 🡪 Carefully Subtract Inequalities Applying Sign of Subtracted From Inequality to the Resulting Inequality
- Last 🡪 Simplify Following Rules of Inequality Manipulation

Видео Inequalities (GMAT Focus Edition – Quantitative Reasoning Content and Tactics) канала AnalystPrep