Absolute value of an integer

The absolute value of an integer is defined as the numerical value with out its sign. The absolute value of an integer is the distance between the number and zero on a number lineand is not considered which direction from zero the number lies.

Example:
The absolute value of |5| = 5
        |-5| = 5
How to Solve Absolute Value Equations
Solve the absolute value equation can be using the following steps.
1. First absolute value is isolated on any one side of the equation.
2. Then write two equations with out absolute symbol or bars.
3. First equation will fix the expression within the absolute value symbol equal to the given expression on the other side of the equal sign.
4. Second equation will fix the provided expression within the absolute value symbol equal to given expression on the other side of the opposite sign.
5. Finally solve the equation and get the solution.
Examples 1:
|2x-1| + 3 =6
First isolate the above equation
|2x-1| = 6-3
|2x-1| = 3
Then write in to two equations with out absolute symbol.
2x-1 = 3 2x-1 = -3
2x = 3+1 2x = -3+1
X = 2 x = -1
The solutions are {-1, 2}

Give some example to solve the Absolute value problems
Example 1:
|3(x+4)| = 24
3(x+4) =24 3(x+4) =-24
3x = 24-12 3x = -24-12
3x = 12 3x = -36
X = 4 x = -12
The solutions are{-12, 4}
Example 2:
6 / |x+3| = 3
First isolate the equation
3|x+3| = 6
3x+9 = 6 3x+9 = -6
3x = -3 3x = -15
X = -1 x = -5
The solutions are {-5, -1}
How to solve the inequalities with absolute value
To solve the inequalities with absolute value first isolate the equation on one side. Then the inequalities can be spilt in to two equations as positive and negative as per properties of the absolute value. Finally solve the equations to get the solution.
Example 1:
|x-1| = 2
X -1 = 2 x-1 = -2
X = 3 x = -1
The solution is -1 = x = 3
Example 2:
|3x+1| = 2x+3
3x+1 = 2x+3 3x+1 = -(2x+3)
3x-2x  = 3-1 3x + 2x = -3-1
X = 2 x = -4/5
The solution is -4/5 = x = 2
The absolute value inequalities

Here some of the absolute value inequalities can be explained with the absolute value equation and picture of real number line.

For example to graph the solution to |x|<5, the solutions of the absolute value of all the point should be less then 5 unit away from the zero. The solution of the absolute value inequalities are -5 < x < 5.

If |x| > 2, the solutions of the absolute value of all the point should be greater then 2 unit away from the zero.  The solution of the absolute value inequalities are -2 > x >