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Absolute Value - Example 4

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.

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Kelly S.

July 23, 2021

so in this type of equation will the answer always be a positive number?

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Missouri State University

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Baylor University

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we're being asked to evaluate to given expression when X is equal to negative seven. Remember to evaluate expressions. We're going to start by substituting negative seven in place of both of our exes. So when we do this, we're gonna have the absolute value off two times negative seven and then minus the absolute value off negative seven plus 10. All right, so now we substitute then to evaluate this expression, we now need to follow the order of operations. Remember, Step One is to evaluate inside our grouping symbols Well, and absolute value is considered to be a grouping. Simple. So the first thing we have to dio is multiply two times negative seven. Well, two times negative seven is negative. 14. So we're left with the absolute value of negative 14. We'll bring down AR minus sign, and then we need to evaluate inside our second absolute value. Simple. Well, negative seven plus 10 is equal deposit of three. So we're left with the absolute value of three. Now that we have evaluated insider absolute value symbols, we have to go ahead and take the absolute value of both of these numbers. Well, the absolute value of negative. 14 is positive. 14 because it's 14 units away on the number line, minus the absolute value of three, while the absolute value of three is equal to three because it's three units away on the number line. And now, as you can see, we only have one operation left. We have 14 minus tree, which is equal to 11. So what we found is the value of our given expression when X is equal to negative, seven is positive 11.

Syracuse University
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Catherine R.

Missouri State University

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Oregon State University

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