Inequalities is an important topic in the GMAT problem solving and GMAT data sufficiency sections. One can expect quite a few questions from this topic. Once the basics are understood and mastered, solving these questions is quite easy. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts
- Explanation to the basic concept of inequalities.
- Various basic rules governing inequalities such as multiplying both sides of an inequality with a negative number, inequalities with algebraic equations such as quadratic expressions, inequalities with exponents, inequalities with modulus.
- 16 solved examples, which also contain additional notes that help solve questions in inequalities quickly.
- 17 exercise problems with the answer key and also explanatory answers.
- An objective type speed test with around 35 questions along with explanatory answers and answer key are provided for the speed test.
Here is an example of a typical solved example in this chapter.
Find the range of values for x for which
As there is a linear term in 'x' in the denominator, we can eliminate the x terms in the denominator by multiplying both sides of the inequality by (x - 2)2
in the numerator
(x - 2) > -2(x - 2)2
=> (x - 2) > -2(x2
- 4x + 4)
=> (x - 2) > -2(2x2
+ 8x - 8)
=> 0 > -2x2
+ 7x - 6
- 4x - 3x + 6 > 0
=> (2x - 3) (x - 2) > 0
The range of values of x that satisfy the above inequality are
In other words, x does not lie between
Looking for additional practice questions in Inequalities? A collection of some questions available at 4GMAT.COM.