SSAT Upper Level Quantitative › How to find absolute value
Evaluate:
Given: are distinct integers such that:
Which of the following could be the least of the three?
only
only
only
or
only
,
, or
, which means that
must be positive.
If is nonnegative, then
. If
is negative, then it follows that
. Either way,
. Therefore,
cannot be the least.
Now examine the statemtn . If
, then
- but we are given that
and
are distinct. Therefore,
is nonzero,
, and
and
.
cannot be the least either.
Define an operation on the real numbers as follows:
If , then
If , then
If , then
If ,
, and
then which of the following is a true statement?
Since , evaluate
, setting
:
Since , then select the pattern
Since , evaluate
, setting
:
, so the correct choice is that
.
The first step to solving is to use the Order of Operations.
The absolute value of a real number x is the non-negative value of x without regard to its sign. The absolute value of a number is the distance of that number from the point of origin or zero on a number line.
There is no solution.
Absolute value measures distance from that number to the point of origin or zero.
However, there is a negative sign outside the Absolute value bars, which indicates the multiplication by
becomes
Therefore is the correct solution.
Which of the following sentences is represented by the equation
The absolute value of the sum of a number and seven is three less than the number.
The absolute value of the sum of a number and seven is three greater than the number.
The sum of three and the absolute value of the sum of a number is three greater than the number.
The sum of three and the absolute value of the sum of a number is three less than the number.
None of the other responses are correct.
is the absolute value of
, which in turn is the sum of a number and seven and a number. Therefore,
can be written as "the absolute value of the sum of a number and seven". Since it is equal to
, it is three less than the number, so the equation that corresponds to the sentence is
"The absolute value of the sum of a number and seven is three less than the number."
Give the solution set:
When dealing with absolute value bars, it is important to understand that whatever is inside of the absolute value bars can be negative or positive. This means that an inequality can be made.
In this particular case if , then, equivalently,
From here, isolate the variable by adding seven to each side.
In interval notation, this is .
Step One: Order of Operations
The absolute value of is
However, because there is a negative sign outside the Absolute value bars, you would multiply the
by
to get the solution.
The correct answer is
Give the solution set:
If , then either
or
. Solve separately:
or
The solution set, in interval notation, is .
Evaluate for :
Substitute 0.6 for :