Algebra II : Absolute Value
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Example Questions
Example Question #21 : Absolute Value
Solve for 
In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.
First multiply both sides by 4.
The absolute value function turns whatever is inside positive, so this has two solutions. 
Next subtract 1 from both sides.
Then, divide by -3.
or
Now subtract 1 from both sides.
Finally, divide both sides by -3
Example Question #22 : Absolute Value
Solve for 
In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.
First, divide both sides by 3.
The absolute value function makes whatever is inside positive, so this has two potential solutions. 
or
Example Question #23 : Absolute Value
If 
If 
Substitute negative seven in for every x.
Recall that the absolute value of a number always becomes positive.
Example Question #24 : Absolute Value
Solve the absolute value equation.
Since absolute values are concerened with the distance from zero, you need two equations to show both possible solutions.
FIRST
SECOND
Example Question #2151 : Mathematical Relationships And Basic Graphs
Solve:
To solve:
1. To clear the absolute value sign, we must split the equation to two possible solution. One solution for the possibility of a positive sign and another for the possibility of a negative sign:
2. solve each equation for 
Example Question #26 : Absolute Value
Solve the following equation for b:
Solve the following equation for b:
Let's begin by subtracting 6 from both sides:
Next, we can get rid of the absolute value signs and make our two equations:
Next, add 13 to both sides
And divide by 5:
or
Next, add 13 to both sides
And divide by 5:
So our answers are
Example Question #21 : Solving Absolute Value Equations
Solve for x:
no solution
no solution
Since the absolute value function only produces positive answers, an absolute value can never be equal to a negative number.
Example Question #28 : Absolute Value
Solve the following equation:
To solve this you need to set up two different equations then solve for x.
The first one is:
The other equations is:
Example Question #29 : Absolute Value
Find values of 
No solution
No solution
Recall the general definition of absolute value,
We will attempt two cases for the absolute value,
Case 1:
Start by isolating the abolute value term,
Replace 
Case 2:
Replace 
Testing the Solutions
Whenever solving equations with an absolute value it is crucuial to check if the solutions work in the original equation. It often occurs that one or both of the solutions will not satisfy the original equation.
For instance, if we test 
This is clearly not true, since both sides are not equal, this rules out 
Example Question #30 : Absolute Value
What are all the possible values of 
If 
Solve each of those equations to find the possible values for x.
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