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.
Solving absolute value equations. Check for extraneous solutions.
|x-3| =9
x=-6 x=12
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.
Solving absolute value equations. Check for extraneous solutions.
|x+4|+3=17
x=-18 x=10
If a is negative what happens to the absolute value function? If a is positive what happens to the absolute value function?
When a is negative the graph points down.
When a is positive the graph points up.
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.
Solving absolute value equations. Check for extraneous solutions.
|2x-3| =4x-1
x= 2/3
Find the vertex of this absolute value function:
y = |x+2| -3
Vertex = (-h, k)
y = a |x+h|+ k
Vertex = (-2, -3)
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, because it represents a distance and distance is always positive.
Solve the equation |3x - 2| = x.
What is x = 1 and x = 0.5.
Solving absolute value equations. Check for extraneous solutions.
|2x| = 3x-1
x=1
Members of a book club agree to read within five pages of the past page of the chapter. The chapter ends on page 150. Write an absolute value equation that represents the pages where club members could stop reading.
|x -150| =5
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.
|x - 6| = 3.
Solving absolute value equations. Check for extraneous solutions.
|4x-1| = 5x + 8
x= -7/9
The temperature of an enclosure for a pet snake should be about 80 degrees F give or take 5 degrees. Write an absolute value equation to find the minimum and maximum temperatures.
|x - 80| = 5