Absolute Value Equations, Part 2. Online Test

The solution set of the equation | 5x - 3 | + | 2x - 1| = | 3x - 2 | is a line segment which length is


The equation | x - 9 | + | x - 4 | = 5 is equivalent to the inequality

2 2


The number of the roots of the equation | | | x - 3 | - 2 | - 1 | = 1 is


The number of integer solutions of the equation

x x

2 2

x - 1 x - 1

=

which satisfy the inequality x < 10 is


The sum of the roots of the equation | x - 3 | x | + 2 | = x - 2x

equals

2 2


The number of the roots of the equation | x - | 2x + 3 | | = 3x - 1 is


The product of the roots of the equation

| 2x - 3 | - | x |

| 3x + 2 | + x - 2

= 5

is


The difference between the greatest and the smallest roots of the equation

| x - x | + 1

| x + 1 | - x

2

2

= 1

equals


If (x, y) is the solution of the system

| x + 1 | - | y + 2 | = - 2,

| x - 2 | + 2y = 3,

then the greatest possible value of | x + y | equals


All the roots of the equation | | 3 - 2x | - 1 | = 2 | x | satisfy the inequality


































Description:

Problems involving absolute values are pretty common for IIT JEE exams. IIT aspirants must be familiar with the notion of absolute value and be fluent in applying various techniques for dealing with this type of problems. This test checks the ability to solve equations involving absolute values. Although almost all the problems could be solved using interval method, in many cases it is time consuming. Try to solve this test yourself. If you find that some of the equations are pretty difficult or time consuming, attend my public class to get advantages of various techniques that allow you to solve these problems effectively in a short period of time.

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Vladimir Louzguine
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Absolute Value Equations, Part 1.
10 Questions | 88 Attempts