All ACT Math Resources
Example Questions
Example Question #1 :How To Find Absolute Value
定义一个操作as follows:
For all real numbers,
Evaluate:.
The expression is undefined.
None of the other responses is correct.
, or, equivalently,
Example Question #11 :How To Find Absolute Value
Define.
Evaluate.
, or, equivalently,
Example Question #1 :Absolute Value
定义一个操作as follows:
For all real numbers,
Evaluate.
Example Question #1 :How To Find Absolute Value
Define.
Evaluate.
Example Question #251 :Integers
定义一个操作as follows:
For all real numbers,
Evaluate
Bothand
Example Question #691 :Arithmetic
What is the minimum value forif?
When solving an absolute value equation, you should remember that you can have either a positive or a negative value in the absolute value. So, for instance:
means thatcan be eitheror.
Thus, for this question, you know thatcan mean:
Then, you just solve each and get:
Thus,is the minimum possible value for.
Example Question #691 :Arithmetic
Simplify.
Begin by simplifying the contents of the absolute value:
Remember that the absolute value of a negative number is a positive value. Thus:
Example Question #182 :Integers
What is the largest possible value forif?
When solving an absolute value equation, you should remember that you can have either a positive or a negative value in the absolute value. So, for instance:
means thatcan be eitheror.
Thus, for this question, you know that. Start by dividing byon both sides. This will give you:
Now, from this, we know:
Solve each equation for. The first is:
The second is. You can tell that this is going to end up being negative. You do not even need to finish. The larger value will be the positive one,.
Example Question #694 :Arithmetic
Evaluate the following expression:
First use order of operations (PEMDAS which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subraction) to evaluate the inner part of the absolute value:
First multiply
.
Then subtract that from.
.
Absolute value means the distance away from zero, and distance is always positive.
Thus:is the answer
Example Question #17 :How To Find Absolute Value
Evaluate the expression ifand.
To solve, we replace each variable with the given value.
Simplify. Remember that terms inside of the absolute value are always positive.