How To Find The Absolute Value Of A Number

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The absolute value of a number is piece of cake to detect, and the theory behind it is important when solving accented value equations. Absolute value ways "distance from naught" on a number line. If you retrieve of a number line, with null in the center, all you're really doing is asking how far away you are from 0 on the number line.

1

Recall that absolute value is a number's distance from nil. An absolute value is the distance from the number to zero along a number line. Simply put, $|-4|$ is just asking you lot how far abroad -iv is from zero. Since distance is always a positive number (yous tin can't travel "negative" steps, simply steps in a different management), the event of absolute value is ever positive.
2

Make the number in the absolute value sign positive. At its most simple, absolute value makes whatever number positive. It is useful for measuring distance, or finding values in finances where yous piece of work with negative numbers like debt or loans.^[one]

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Use uncomplicated, vertical bars to evidence accented value. The notation for absolute value is easy. Unmarried bars (or a "pipe" on a keyboard, found near the enter cardinal) effectually a number or expression, similar $|n|,|3+5|,|-72|$ , indicates accented value.
- $|2|$ is read as "the absolute value of ii."^[2]
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Driblet any negative signs on the number inside the accented value marks. For case, |-5| would become |5|.
v
Drop the absolute value marks. The number remaining is your respond, so |-five| becomes |five| and then v. This is all you lot demand to practice^[3]
- $|-5|=v$
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Simplify the expression inside the absolute value sign. If you've got a elementary expression, like $|-10|$ , you tin can just brand the whole thing positive. But expressions similar $|(-iv*5)+3-2|$ need to be simplified before you can take the absolute value. The normal gild of operations still applies:
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Always utilize the guild of operations before finding absolute value. When determining longer equations, yous want to do all the possible work before finding the absolute value. You should not simplify absolute values until everything else has been added, subtracted, and divided successfully. For example:
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Go along working on some exercise problems to go it downwards. Absolute value is pretty easy, merely that doesn't mean a few practice problems won't assist you keep the knowledge:

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Note whatsoever complex equations with imaginary numbers, similar "i" or ${\sqrt {-one}}$ and solve separately. You cannot find the absolute value of imaginary numbers the same way you plant it for rational numbers. That said, y'all can easily find the absolute value of a circuitous equation by plugging it into the distance formula. Take the expression $|3-4i|$ , for case.
2

Discover the coefficients of the complex equation. Call up of iii-4i as an equation for a line. Absolute value is the distance from cypher, and then yous want to observe the altitude from zero for the betoken (3, -iv) on this line.The coefficients are simply the two numbers that aren't "i." While the number by the i is usually the second number, it doesn't actually matter when solving. To practise, observe the post-obit coefficients:
3

Remove the accented value signs from the equation. All yous need at this point are the coefficients. Retrieve, you need to discover the distance from the equation to goose egg. Since you lot use the distance formula in the next step, this is the same thing as taking absolute value.
4

Square both coefficients. To find distance, you'll use the distance formula, known every bit ${\sqrt {x^{two}+y^{two}}}$ . Then, for your first stride, yous demand to foursquare both coefficients of your complex equation. Continuing the example $|3-4i|$ :
v

Add the squared numbers under the radical. The radical is the sign that takes the square root. Only add them up, leaving the radical in identify for now.
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Accept the square root to get your last answer. All you have to do is simplify the equation to get your terminal answer. This is the altitude from your "point" on an imaginary graph zero. If in that location is no square root, just leave the respond from the last step under the radical-- this is a legitimate final respond.
vii

Endeavour a few practise bug. Utilize your mouse to click and highlight right after the questions to see the answers, written hither in white.

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Question

What is the absolute value of -(-2)?

-(-two) = +2. The absolute value is 2.
Question

What is the accented value of 2 * ii/2?

|[(2)(2)] / two| = |4/2| = |2| = 2.
Question

How do I observe the value of f(-1) if f(x) = 7 squared + 2x +xiv?

Substitute (-1) for each x in the expression. Y'all have written f(x) = 7² + 2x + xiv. That simplifies to 2x + 63. Substituting (-1) for x makes f(-1) = (-2) + 63 = 61. If you meant to write that f(x) = 7x² + 2x + 14, then f(-1) = 7(-1)² + 2(-1) + xiv = vii - ii + fourteen = 19.
Question

What is the accented value of 7?

|vii| = 7.
Question

The number 41386 is given. In a different number, the eight represents a value of the 8 in 41386. What value is represented past the viii in the other numbers?

In the given number the 8 represents a value of eighty.
Question

What is the absolute value of 3 - √26?

3 - √26 = -2.1. The accented value of -2.1 is 2.ane.

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If you lot accept a variable inside absolute value marks, you can't remove the marks using this method because if the value of the variable is negative, the absolute value would brand it positive.
If yous have an expression inside absolute value marks, simplify the expression earlier finding the accented value.
When a positive number is inside absolute value marks, the answer is always that number.
You demand a unlike method to solve absolute value equations involving x and y, though they apply the theory backside accented value as its base.
An absolute value can never equal to a negative number so if y'all see something like this | 2 - 4x| = -7 know that this equation is not true fifty-fifty without solving.

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Article Summary X

The accented value of a number is the number's distance from zero, which will e'er be a positive value. To find the absolute value of a number, drop the negative sign if there is 1 to make the number positive. For instance, negative 4 would become 4. If y'all accept a complicated equation, simplify it using the order of operations earlier you drib the negative signs. The symbol for an absolute number is vertical lines on either side of the number. For more tips, including how to find the accented value in an equation with "I", read on!

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