Absolute Value Concepts

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What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line, regardless of direction.

What is the absolute value of -7?

The absolute value of -7 is 7.

If the absolute value of a number is 10, what are the possible original numbers?

The original numbers could be 10 or -10.

How do you denote the absolute value of a number 'x'?

The absolute value of 'x' is denoted as |x|.

What is |0| equal to?

|0| equals 0 because zero is zero units away from itself on the number line.

What is the absolute value of 15 minus the absolute value of -5?

The absolute value of 15 is 15, and the absolute value of -5 is 5, so 15 - 5 = 10.

What happens to a negative number inside absolute value symbols?

A negative number turns into a positive number, reflecting its distance from zero.

Solve: |-12| + |7|.

|-12| is 12 and |7| is 7, so the answer is 19.

What is the absolute value of |3 - 5|?

3 - 5 equals -2, and |-2| is 2.

Compare: Which is greater, |-6| or |3|?

|-6| is 6 and |3| is 3. So |-6| is greater.

What is the absolute value of the expression |–x| when x is positive?

If x is positive, then –x is negative, but |–x| changes it back to positive, making it equal to x.

True or False: The absolute value of any real number is always positive.

True, except for the absolute value of zero, which is zero.

Find the absolute value of a sum: |5 + (-8)|.

5 + (-8) equals -3, so the absolute value |–3| is 3.

Solve for x if |x| = 9.

x could be 9 or -9.

When graphing, what does the absolute value symbol tell us about the number's position?

It tells us the number's distance from zero, not its direction.





Test Your Knowledge

Select the correct option


1. What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line, regardless of direction.

The negative of a number in all cases.

The value of a number on a number line with direction.

The oppositional force on a gravitational object.

2. What is the absolute value of -7?

The absolute value of -7 is 7.

The absolute value of -7 is -7.

The absolute value of -7 is -3.5.

The absolute value of -7 is 0.

3. If the absolute value of a number is 10, what are the possible original numbers?

The original number could be 0 or 10.

The original numbers could be 20 or 0.

The original numbers could be 10 or -10.

The original numbers could be 5 or -5.

4. How do you denote the absolute value of a number 'x'?

The absolute value of 'x' is denoted as |x|.

The absolute value of 'x' is denoted as x*.

The absolute value of 'x' is denoted as *x*.

The absolute value of 'x' is denoted as x|.

5. What is |0| equal to?

|0| equals -1 because zero is one unit away from any other number.

|0| equals 1.

|0| equals 0 because zero is zero units away from itself on the number line.

|0| equals 10, assuming all numbers round to a base unit of ten.

6. What is the absolute value of 15 minus the absolute value of -5?

15 - (-5) = 20

15 - 5 = 10

15 + 5 = 20

15 - 5 = 0

7. What happens to a negative number inside absolute value symbols?

A negative number turns into a positive number, reflecting its distance from zero.

A negative number remains negative.

A negative number doubles its magnitude.

A negative number has no definable absolute value.

8. Solve: |-12| + |7|.

|-12| + |7| = 7

|-12| + |7| = 5

|-12| + |7| = 19

|-12| + |7| = -5

9. What is the absolute value of \n |3 - 5|?

3 - 5 equals -2, and |-2| is 2.

3 - 5 equals -8, so |-8| is 8.

3 - 5 equals 2, so |2| is 2.

3 - 5 equals 0, so |0| is 0.

10. Compare: Which is greater, |-6| or |3|?

|-6| is 6 and |3| is 3. So |-6| is greater.

|-6| is 0 and |3| is 3. So |3| is greater.

|-6| is -6 and |3| is 3. So |3| is greater.

Both are equal.

11. What is the absolute value of the expression |–x| when x is positive?

If x is positive, then –x is negative, but |–x| changes it back to positive, making it equal to x.

If x is positive, then |–x| is twice x.

If x is positive, the result is always negative.

If x is positive, then |–x| is undefined.

12. True or False: The absolute value of any real number is always positive.

True, except for the absolute value of zero, which is zero.

False, it can be negative.

False, the absolute value is always zero.

True, without exception.

13. Find the absolute value of a sum: |5 + (-8)|.

5 + (-8) equals -3, so the absolute value |–3| is 3.

5 + (-8) equals -3, so the absolute value |–3| is -3.

5 + (-8) equals -13, so the absolute value |-13| is 13.

5 + (-8) equals -3, so the absolute value |–3| is 0.

14. Solve for x if |x| = 9.

x could be 0 or 9.

x could be 9 or -9.

x is always 9.

x could be any positive number.

15. When graphing, what does the absolute value symbol tell us about the number's position?

It tells us the number's distance from zero, not its direction.

It determines the number's direction on the graph.

It indicates if a number is greater or lesser than another.

It converts all numbers to zero on the graph.