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# First Degree Absolute Value Equation Examples

### First Degree Absolute Value Equation Example 1

Question:
Solving the equation | 5x | = 35
The property of the absolute value equation:
Let a be a real number,
(i) If a is positive, then the equation | x | = a is equivalent to x = - a or x = a
(ii) If a is negative, then the equation | x | = a has no solution.
(iii) If a = 0, then the equation | x | = 0 is equivalent to x = 0.
Solution>
| 5x | = 35
5x = - 35 or 5x = 35
x = - 7 or x = 7
Therefore, the equation | 5x | = 35 has two solution x = - 7 or x = 7

### First Degree Absolute Value Equation Example 2

Question:
Solving the equation 7| x - 6 | = 63
Solution:
7 | x - 6 | = 63 , both sides divide by 7
| x - 6 | = 9
The property of the absolute value equation is:
If a is positive number, then the equation | x | = a is equivalent to x = - a or x = a
Then the solution of | x - 6 | = 9 is:
x - 6 = - 9 or x - 6 = 9
x = 6 - 9 or x = 6 + 9
x = - 3 or x = 15
Therefore, the equation 7 | x - 6 | = 63 has two solution x = - 3 or x = 15

### First Degree Absolute Value Equation Example 3

Question:
Solving the equation | 1 - 2x | = 9
Solution:
The property of the absolute value equation is:
If a is positive number, then the equation | x | = a is equivalent to x = - a or x = a
Then the solution of | 1 - 2x | = 9 is:
1 - 2x = - 9 or 1 - 2x = 9
- 2x = -1 - 9 or - 2x = - 1 + 9
- 2x = - 10 or - 2x = 8
- x = - 5 or - x = 4
x = 5 or x = - 4
Therefore, the equation | 1 - 2x | = 9 has two solution x = 5 or x = - 4

### First Degree Absolute Value Equation Example 4

Question:
Solving the equation | 5x - 3 | = | x + 9 |
Solution:
The property of the absolute value equation is:
If a is positive number, then the equation | x | = a is equivalent to x = - a or x = a
Then the solution of | 5x - 3 | = | x + 9 | is:
5x - 3 = - ( x + 9 ) or 5x - 3 = + ( x + 9 )
5x - 3 = - x - 9 or 5x - 3 = x + 9
5x + x = 3 - 9 or 5x - x = 3 + 9
6x = - 6 or 4x = 12
x = - 1 or x = 3
Therefore, the equation | 5x - 3 | = | x + 9 | has two solution x = - 1 or x = 3

### First Degree Absolute Value Equation Example 5

Question:
Solving the equation | 5x - 8 | = | 3x + 2 |
Solution:
The property of the absolute value equation is:
If a is positive number, then the equation | x | = a is equivalent to x = - a or x = a
Then the solution of | 5x - 8 | = | 3x + 2 | is:
5x - 8 = - ( 3x + 2 ) or 5x - 8 = + ( 3x + 2)
5x - 8 = - 3x - 2 or 5x - 8 = 3x + 2
5x + 3x = 8 - 2 or 5x - 3x = 8 + 2
8x = 6 or 2x = 10
x = 6/8 = 3/4 or x = 5
Therefore, the equation | 5x - 8 | = | 3x + 2 | has two solution x = 3/4 or x = 5