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Chapter 0: Problem 36

Find each sum or difference. $$ |-7-15| $$

Short Answer

Expert verified
The answer is 22.

Step by step solution

01

Understand the Absolute Value

The absolute value of a number is the distance between that number and zero on a number line. It is always non-negative. The absolute value of a number is denoted by two vertical bars, such as \( |a| \).
02

Simplify the Expression Inside the Absolute Value

Simplify the expression inside the absolute value before finding the absolute value. In this case, the expression is \(-7 - 15\).
03

Perform the Subtraction

Subtract 15 from -7: \(-7 - 15 = -22\).
04

Apply the Absolute Value

Take the absolute value of -22. Since the absolute value is the distance from zero, \( |-22| = 22 \).

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Key Concepts

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

headline of the respective core concept
Absolute value is a fundamental concept in algebra. It represents the distance a number is from zero on a number line. This distance is always non-negative. We denote absolute value with two vertical bars, like this: \(|a|\). It doesn't matter whether the number is positive or negative; the absolute value will always be positive. For example, \(|-7|\) equals 7, and \(|15|\) equals 15. So, remember, absolute value helps you focus just on the magnitude, not the direction, of a number.
headline of the respective core concept
A number line is a visual way of representing numbers. It's like a ruler where integers, fractions, and decimals find a place. Each point on the number line corresponds to a number. The number line is incredibly useful for understanding absolute value because it clearly shows the distance of any number from zero.

When you have negative and positive numbers, they are placed on the left and right of zero, respectively. For instance, in the exercise, you see how -22 and 22 are both 22 units away from zero. Understanding this layout makes it simpler to grasp why the absolute value of any number is always positive.
headline of the respective core concept
Subtraction is one of the basic arithmetic operations where you find the difference between two numbers. In algebra, it's crucial to follow the correct order of operations. In our exercise, you perform the subtraction first before applying the absolute value.

Let's walk through the steps again briefly: You start with \(-7 - 15\). Here, subtracting 15 from -7 gives you -22. Subtraction worked through here ensured we simplified the expression first. Finally, when you take the absolute value of -22, you get 22. This process shows that no matter how complex the subtraction within the absolute value brackets, the final absolute value will always be non-negative.

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Most popular questions from this chapter

Use an inequality symbol to write each statement. $$ 13-3 \text { is less than or equal to } 10 . $$

Simplify each expression. $$ -14\left(-\frac{2}{7}\right) \div(2 \cdot 6-10) $$

Evaluate each expression for \(a=-3, b=64,\) and \(c=6 .\) $$ \sqrt{b}-c+a $$

Write each fraction as a decimal. For repeating decimals, write the answer by first using bar notation and then rounding to the nearest thousandth. See Example 11. $$ \frac{8}{9} $$

Simplify each inequality if needed. Then determine whether the statement is true or false. $$ -8>-|-6| $$
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