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# First Degree Absolute Value Equation Examples

# First Degree Absolute Value Equation Example 1

# First Degree Absolute Value Equation Example 2

# First Degree Absolute Value Equation Example 3

# First Degree Absolute Value Equation Example 4

# First Degree Absolute Value Equation Example 5

- 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

- 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

- 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

- 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

- 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