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Example Questions
Example Question #3 : Absolute Value
Example Question #14 : Algebra Ii
Solve:
All real numbers
No solution
The absolute value can never be negative, so the equation is ONLY valid at zero.
The equation to solve becomes .
Example Question #11 : Algebra Ii
Solve for :
To solve absolute value equations, we must understand that the absoute value function makes a value positive. So when we are solving these problems, we must consider two scenarios, one where the value is positive and one where the value is negative.
and
This gives us:
and
However, this question has an outside of the absolute value expression, in this case
. Thus, any negative value of
will make the right side of the equation equal to a negative number, which cannot be true for an absolute value expression. Thus,
is an extraneous solution, as
cannot equal a negative number.
Our final solution is then
Example Question #12 : Algebra Ii
Solve for .
Divide both sides by 3.
Consider both the negative and positive values for the absolute value term.
Subtract 2 from both sides to solve both scenarios for .
Example Question #13 : Algebra Ii
Find the -intercepts for the graph given by the equation:
To find the -intercepts, we must set
.
To solve absolute value equations, we must understand that the absoute value function makes a value positive. So when we are solving these problems, we must consider two scenarios, one where the value is positive and one where the value is negative.
Now we must set up our two scenarios:
and
and
and
Example Question #1 : Understanding Imaginary And Complex Numbers
Simplify the radical.
No solution
First, factor the term in the radical.
Now, we can simplify.
Example Question #2 : Understanding Imaginary And Complex Numbers
Multiply:
FOIL:
Example Question #1 : Imaginary Numbers
Multiply:
Since and
are conmplex conjugates, they can be multiplied according to the following pattern:
Example Question #1 : Imaginary Numbers
Multiply:
Since and
are conmplex conjugates, they can be multiplied according to the following pattern:
Example Question #5 : Understanding Imaginary And Complex Numbers
Evaluate:
can be evaluated by dividing
by 4 and noting the remainder. Since
- that is, since dividing 45 by 4 yields remainder 1:
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