Pre-Algebra : Operations
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Example Questions
Example Question #361 : Operations
Fill in the blank using 
The term 
So, we can rewrite the orignal problem as
and we can easily see that
Example Question #362 : Operations
Compare the following using
The absolute value of a number is the distance that number is from zero on a number. Because it is a distance, the absolute value can never be negative. So,
can be written as
Therefore, it's easy to solve.
Example Question #363 : Operations
Simplify the following expression:
Simplify the following expression:
Let's begin by focusing on the inside of the absolute value signs:
However, because we are within the absolute value signs, we need to change the negative sign to a positive one.
Anytime you have something within the absolute value sign, you need to make it positive.
Our answer is 6.
Example Question #361 : Operations And Properties
Simplify the following:
None of the above
It is important to be careful of where the negative sign is when simplifying.
When simplifying you should end up with:
Example Question #363 : Operations
Solve for x in the following equation:
The absolute value is defined as the distance that number is from zero on the number line. Because it is a distance, the absolute value cannot be negative. So, in the equation
we look at the absolute value.
because -9 is 9 units from zero. Now, we can solve for x.
Example Question #366 : Operations
Compare the following using
Absolute values are defined as the distance the number is from zero on a number line. Because it is a distance, the absolute value cannot be negative. So,
because -9 is 9 units from zero on a number line. So,
can easily be solved as
Example Question #362 : Operations And Properties
The symbol | | around each real number signifies absolute value. Absolute value is the true magnitude of a real number, without looking at the positive or negative sign attached to it. To rewrite this problem when solving, remove all absolute value symbols as well as signs.
Example Question #363 : Operations And Properties
Solve the following:
The absolute value of a number is defined as the position or distance of the number from zero on the number. Because it is a distance, the value cannot be negative. So,
and
so
Example Question #364 : Operations And Properties
If 
Substitute 5 for 
Remember that the absolute value of a number is its distance from zero on a number line. Distance is always positive; therefore, you can rewrite the expression.
Subtracting a positive number from a negative number is the same as adding a negative number.
Solve.
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