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Chapter 1: Problem 61

Find each absolute value. \(-|6-3|\)

Short Answer

Expert verified
-3

Step by step solution

01

Simplify Inside the Absolute Value

First, subtract the numbers inside the absolute value: Subtraction: \(6 - 3 = 3\)
02

Apply Absolute Value

Next, find the absolute value of the result: \(|3| = 3\)
03

Apply the Negative Sign

Finally, apply the negative sign outside the absolute value: \(-|3| = -3\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

absolute value
The absolute value of a number measures how far that number is from zero on a number line, regardless of direction.
In simpler terms, it's the non-negative version of any given number. For example, the absolute value of both 5 and -5 is 5 because they are both five units away from zero.
We denote absolute value using vertical bars, like this: \(|x|\). So, \(||3|| = 3\) and \(||-3|| = 3\). Absolute value essentially 'removes' any negative sign in front of a number, converting it to its positive counterpart.
subtraction inside absolute value
The core idea behind subtraction inside absolute value is to simplify the expression under the absolute value first.
In our example, we have \(6 - 3\). We need to perform this subtraction before applying the absolute value.
\((6 - 3 = 3)\).
Now, we replace the original inside of the absolute value with 3, resulting in \(|3|\).
Always make sure to simplify expressions inside the absolute value before anything else.
negative sign application
Once we have simplified the expression within the absolute value and found its absolute value, we can apply any additional operations.
Our example ends with a negative sign outside the absolute value: \(-|6-3|\).
After getting the absolute value, which is 3, the last step is to apply the negative sign: \(-|3| = -3\).
Remember, the absolute value operation always comes before applying any outside operations, like adding or subtracting a sign.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 12 if it is divisible by both 3 and \(4,\) and not otherwise. (a) Is 4,249,474 divisible by \(12 ?\) (b) Is 4,253,520 divisible by \(12 ?\)

Write a numerical expression for each phrase, and simplify the expression. 8 less than -2

Use the distributive property to rewrite each expression. $$ 8(x-6) $$

Solve each problem. A pilot announces to the passengers that the current altitude of their plane is \(34,000 \mathrm{ft}\). Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(5 x-2 y+3 a\)
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