Absolute Value Equation
Absolute Value Equation The equation |x| = 4. This means that x could be 4 or x could
be -4.
When you take the absolute value of 4, the solution is 4 and when you take the
absolute value of -4, the solution is also 4. An absolute value problem, you have to get
into account that there can be two solutions that wil make the equation true.
Learning absolute value equation, you set the quantity inside the absolute value symbol
equal to the positive and negative value on the other side of the equal symbol.

Solve Absolute Value Equations
Below are the examples on how to solve absolute value equations -
Example 1:
|x + 1| = 4


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Solution:
The quantity inside the absolute value symbol can be equal to 4 or -4
x + 1 = 4 or x + 1 = - 4
Subtract 1 on both side of the given equation
x + 1 - 1 = 4 - 1 or x + 1 - 1 = -4 - 1
x = 3 or x = -5
So the solution are x = 3 and x = -5
Example 2:
|2x - 3| = x - 5
Solution:
When solving this equation, you have to be careful when solving opposite of (x - 5)
2x - 3 = x - 5 or 2x - 3 = -(x - 5)
So, the solution is x = -2 and x = 83

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x - 3 = -5 or 2x -3 = -x + 5
x = -2 or 3x - 3 = 5
3x = 8
x =
So, the solution is x = -2 and x = 83
Example 3:
|x + 1| = 5
Solution:
The quantity inside the absolute value symbol can be equal to 5 or -5
x + 1 = 5 or x + 1 = -5
Subtract 1 on both side of the given equation
x + 1 - 1 = 5 - 1 or x + 1 - 1 = - 5 - 1
x = 4 or x = - 6

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What is a Dependant Variable
What is a dependent variable?
Dependent variable define as the variable whose value is based on the value of other
variable in its equation.
That is the value of dependent variable is always said to be dependent on the
independent variable of math equation.
For example, consider the equation y = 4x + 3. In this equation the value of the variable
`y' value changes according to the changes in the value of `x'. Therefore the variable `y'
is said to be as dependent variable. Some of the examples that involve dependent
variables are discussed in detail as below with their solutions.

Dependent Variable Examples
Below you can see the solved dependent variable examples -

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Example 1:
Find the value of y in the fol owing equation, y = 3x2 + 2x + 4 when the value of x is
equal to 3.
Solution:
Given equation:
y = 3x2 + 2x + 4
Now substitute the value of x as 3 in the given equation
y = 3(3)2 + 2(3) + 4
Solving the equation we get,
y = 3(9) + 2(3) + 4
y = 27 + 6 + 4
y = 37
Therefore the `y' is said to be as dependent variable and `x' is said to be as independent
variable.


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