How to find absolute value

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SSAT Upper Level Quantitative › How to find absolute value

Questions 1 - 10
1

Evaluate:

Explanation

2

Given: are distinct integers such that:

Which of the following could be the least of the three?

only

only

only

or only

, , or

Explanation

, 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.

3

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?

Explanation

Since , evaluate

, setting :

Since , then select the pattern

Since , evaluate

, setting :

, so the correct choice is that .

4

Explanation

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.

5

There is no solution.

Explanation

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.

6

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.

Explanation

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."

7

Give the solution set:

Explanation

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 .

8

Explanation

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

9

Give the solution set:

Explanation

If , then either or . Solve separately:

or

The solution set, in interval notation, is .

10

Evaluate for :

Explanation

Substitute 0.6 for :

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