Rewriting Absolute Value Equations
Rewrite the absolute value equation as two linear equations: 3|5x + 11| = 6
5x + 11 = 2 and 5x + 11 = -2
Solve the equation:
|x + 3| = 5
x = 2 and x = -8
Solve the equation
|1 - 2/3x| = 9
x = -12 and x = 15
What is absolute value?
The distance of a number from zero.
Rewrite the absolute value equation as two linear equations: |3x - 6| - 9 = -3
3x - 6 = 6 and 3x - 6 = -6
Solve the equation
|2x + 6| = 14
x = 4 and x = -10
Solve the equation
|x - 2| + 6 = 0
What is you cannot solve, therefore no solution.
Solving absolute value equations.
|x-3| =9
x=-6 x=12
Rewrite the absolute value equation as two linear equations: 2|x - 1/2|+5 = 15
x - 1/2 = 5 and x - 1/2 = -5
Solve the equation
|1/2x - 4| = 1
x = 10 and x = 6
Solve the equation
|x + 3| - 1 = 0
x = -2 and x = -4
Solving absolute value equations.
|x+4|+3=17
x=-18 x=10
Rewrite the absolute value equation as two linear equations: 1/2|6x - 3| = 9
6x - 3= 18 and 6x - 3= -18
Solve the equation
|4 - 5x| = -6
No solution. Absolute value equations cannot equal a negative number.
Solve the equation
|3x - 2| = x
x = 1 and x = 0.5.
Explain why an absolute value cannot be set equal to a negative value.
Because absolute values always result in a positive number.
Rewrite the absolute value equation as two linear equations: 4/3|3x - 1|+2 = 6
3x - 1= 3 and 3x - 1= -3
Solve the equation
|3x - 6| - 9 = -3
x = 0 and x = 4
Write an absolute value equation that has the given solutions: 3 and 9
Example: |x - 6| = 3
What are the two set ups to solve this equations?
|2x+3|=4x-1
2x+3=4x-1 or 2x+3=-(4x-1)