Solving Absolute Value Equations
1. Change subtraction to adding the opposite. (Keep Change Opposite)
2. Get the absolute value function alone by:
--Adding or subtracting the non-variable number that is
outside of the absolute value function from both sides.
--Dividing both sides by the coefficient of the absolute value function or
multiplying both sides by the reciprocal of the coefficient.
3. If it equals a positive number, the expression inside the absolute value function
has two possible solutions.
--One for when the expression inside evaluates to a negative number
because the absolute value of a negative number is positive and
--One for when the expression inside evaluates to a positive number because
the absolute value of a positive number is positive as well.
4. If the absolute value function equals a negative number, then the equation has
no solution because the absolute value of a number is always positive.
Step by Step Solution for
Two Solutions
Because
6  6 and  6  6
 13  2 2 x  4  25
Step 1.
 13  2 2 x  4  25
Step 2.
 13   2 2 x  4  25
 13
 13

2 2x  4
2

 12
2
2x  4  6
Step 3.
2x  4  6
2 x  4  6
44
4 4
2x
2

2
2
x 1
or
2x
 10

2
2
x  5
Therefore, it has two solutions
x = 1 or x = -5