# Absolute Value (2023)

## FAQs

### What is the absolute value of answers? ›

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

How many answers should you get for an absolute value problem? ›

An absolute value equation may have one solution, two solutions, or no solutions.

Is there always two answers for absolute value? ›

In conclusion, an absolute-value problem will not always have two solutions, because absolute-value inequalities result in one set of solutions. If the problem contains only one absolute number, it will have only one solution and that will be the positive number.

Do you have to check your answers for absolute value equations? ›

Second, if the absolute value equation is of the form , we don't need to check for any solutions at all. This is because an absolute value expression can never be negative, so there will never be a solution for an equation of this form.

What is the absolute value of 16 answer? ›

What is the absolute value of − 6 responses? ›

|–6| = 6 means “the absolute value of –6 is 6.”

What is the easiest way to find absolute value? ›

The absolute value of the number is defined as its distance from the origin. For example, to find the absolute value of 7, locate 7 on the real line and then find its distance from the origin. To find the absolute value of −7, locate −7 on the real line and then find its distance from the origin.

What are the rules of absolute value equations? ›

To solve an equation containing absolute value, isolate the absolute value on one side of the equation. Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

Is the absolute value of a number always positive answer? ›

The absolute value of a number or integer is the actual distance of the integer from zero, in a number line. Therefore, the absolute value is always a positive value and not a negative number.

How many possible answers are there when solving equations involving absolute value? ›

This should make sense when you graph the line y=5 over the absolute value function graph because you can see that there are two intersection points, and thus two solutions. Absolute value functions can have up to two solutions! Now you know that ABSOLUTE VALUE EQUATIONS CAN HAVE TWO SOLUTIONS.

### What makes an absolute value equation false? ›

There's one MAJOR red flag of an equation with an absolute value that has no solution. Recall that an absolute value expression can never be less than zero. That is, a fully reduced absolute value expression must be greater than or equal to zero.

Why do some absolute value equations have one solution? ›

When the right hand side of the equation is zero, then the absolute value equation has only one solution. Therefore, the absolute value equation has only one solution.

What is the absolute value of 8 answer? ›

So, the absolute value of is, 8 = 8.

What is the absolute value of 9 answer? ›

The absolute value of a number tells only one thing: 1. distance from 0. The absolute value of 9 is 9. (9 is 9 places from 0.)

What is the absolute value of 10 answer? ›

In the case of the absolute value of 10, or |10|, we have that 10 is positive, so the absolute value of 10 is 10. Geometrically speaking, we define the absolute value of a number x as the distance x is from 0 on the number line.

What is the absolute value of 4 responses? ›

Answer and Explanation: The absolute value of 4 is 4. The formal definition of the absolute value of a number x, denoted |x|, is the distance that x is from 0 on a number line. Since distance is always positive, we see that taking the absolute value of a number is the same as taking the positive value of that number.

What is the absolute value of 25? ›

The distance from 25 to 0 is 5 units . That means the absolute value of 25 is 5 .

What is the absolute value of 23? ›

The absolute value of a number is the distance of that number from zero. The absolute value of 23 is 23 because it is 23 units from zero.

Can you have a negative answer with absolute value? ›

Since the absolute value of any number other than zero is positive, it is not permissible to set an absolute value expression equal to a negative number.

What is an example of a no solution? ›

As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.

### What can absolute value not be? ›

Absolute value gives distance, but discards information about direction. Because direction is ignored, the absolute value of any number can only be positive or zero, never negative.

What is the absolute value of 65? ›

The absolute value of 65 is65.

What is the absolute value of 17? ›

The absolute value of 17 is "17" because the absolute value of 17 is seventeen units away from zero on the number line. In another way, |17| indicates that the absolute value of 17 is 17.

What is the absolute value in Algebra 2? ›

Every real number is either positive or negative. The two numerals +7 and -7 have different signs but the numerical part of each is 7. This part of the numeral designates the absolute value of the number. The absolute value of a is denoted by | a | (a vertical bar on each side of the quantity).

Can absolute value have infinite solutions? ›

Yes, it can; for example, |x|=x has the solution set [0,∞) , which contains infinitely many solutions.

How many solutions can an absolute value inequality have? ›

Absolute value equations can have up to two solutions. To solve an absolute value inequality involving “less than,” such as |X|≤p, replace it with the compound inequality −p≤X≤p and then solve as usual.

What is the absolute value of 12? ›

It's easy to understand that the absolute value of 12 and -12 are identical: they're both 12, since each number is 12 units away from zero. Absolute value is always positive — to get the absolute value of a negative number, just take away the minus sign.

What is the absolute value of 11? ›

The absolute value of any positive number is the number itself, so 11 has 11 as an absolute value.

Is absolute value always true? ›

The absolute value of any number is either positive or zero. An absolute value equation is never true if it is asserting that the absolute value is negative. The absolute value equation is sometimes true when it is asserted that the absolute value is zero.

Is Infinity bigger than absolute Infinity? ›

The Absolute Infinite (symbol: Ω) is an extension of the idea of infinity proposed by mathematician Georg Cantor. It can be thought of as a number that is bigger than any other conceivable or inconceivable quantity, either finite or transfinite.

### Do all numbers have an absolute value? ›

The absolute value of a number is equal to the distance between that number and zero on a number line. Since distance cannot be negative, this means that all numbers have an absolute value that is positive or equal to zero.

What are the 3 steps to solving absolute value equations? ›

Step 1: Isolate the absolute value|3x - 6| - 9 = -3 |3x - 6| = 6
Step 2: Is the number on the other side of the equation negative?No, it's a positive number, 6, so continue on to step 3
Step 3: Write two equations without absolute value bars3x - 6 = 6
Step 4: Solve both equations3x - 6 = 6 3x = 12 x = 4

What are true facts about absolute value? ›

absolute value, Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number a is positive or zero, its absolute value is itself.

What makes an absolute value equation all real numbers? ›

If the absolute value is greater than or greater than or equal to a negative number, the solution is all real numbers. The absolute value of something will always be greater than a negative number.

Are absolute value functions never one to one? ›

For example, the absolute value function |x| is not one-to- one as a function from the reals to the reals. However, it is one-to-one as a function from the natural numbers to the natural numbers.

What is the absolute value of |- 2 |? *? ›

For example, |-2| = 2. Irrespective of the sign of the numeric value, the absolute value is always non-negative.

What is the absolute value of |- 9 |? A? ›

The absolute value of a number tells only one thing: 1. distance from 0. The absolute value of 9 is 9.

What's the absolute value of 4? ›

The absolute value of 4 is 4 and –3 is 3. Subtract the smaller number from the larger and you get 4 – 3 = 1. The larger absolute value in the equation was 4 or a positive number so you give the result a positive result.

What is the absolute of 2? ›

For example,|2| represents the absolute value of 2.

What is the absolute value of 50? ›

So we would say the absolute value of negative 50 is 50, and the absolute value of five is five.

### What's the absolute value of 3? ›

For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.

What is the absolute value of 35 _____? ›

Answer: =》Absolute value of any number is positive. Here, The absolute value of (-35) is 35.

What is the absolute value of 64? ›

We recall that the absolute value of any number is the distance of that number from zero. This means that the directional sign doesn't matter and the absolute value of a number is never negative. The absolute value of negative 64 is therefore equal to 64, as negative 64 is 64 away from zero.

What is the absolute value of 11 answer? ›

The absolute value of any positive number is the number itself, so 11 has 11 as an absolute value.

What is the absolute of 100? ›

So, the absolute value of is, 100 = 100.

What is the value of |- 13? ›

The absolute value of -13 is -13.

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