Problem 53 Evaluate each expression. $$|1... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 53

Evaluate each expression. $$|15-7+3|$$

Short Answer

Expert verified

Step by step solution

Simplify Inside the Absolute Value

First, perform the arithmetic operation inside the absolute value. Evaluate the expression inside the absolute value a) Subtract 7 from 15: $|15 - 7 + 3| = |8 + 3|$

Complete the Arithmetic Operation

Next, add the remaining number: $8 + 3$ 12

Apply the Absolute Value

Finally, apply the absolute value. The absolute value of a number represents its distance from zero, which is always non-negative: $|12| = 12$

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Key Concepts

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

Arithmetic Operations

Let's break down what happens in the given exercise through arithmetic operations. Arithmetic operations include addition, subtraction, multiplication, and division. In this exercise, we focus on addition and subtraction. First, we examine the expression inside the absolute value:

$ |15-7+3| $, starting with subtraction. Subtracting is finding the difference between numbers by taking away one number from another. Here, we subtract 7 from 15, which simplifies to:

$ 15-7 = 8 $.
Next, we add the number 3 to the result:

$ 8+3 = 11 $. Adding means combining numbers to create a sum. Remember, the correct order of operations helps ensure your calculations are accurate.

Simplifying Expressions

Simplifying expressions involves performing operations to break down a mathematical expression into a more manageable form. In this exercise, the expression

$ |15-7+3| $ is simplified through a series of steps. By performing operations inside the absolute value, we gradually find a simpler expression:

First, calculate

$ 15-7 $ to get 8.
Then, add 3 to 8, resulting in 11.

Simplifying expressions helps us focus on understanding and solving the core problem efficiently. Each step in the solution leads us closer to the final answer by making the math simpler and easier to follow.

Distance from Zero

Absolute value represents the distance from zero on the number line, turning all numbers into their non-negative form. In this exercise, once the arithmetic inside the absolute value is complete, we find

$ |8+3| = |11| $. Distance from zero means how far a number is from zero, regardless of its direction (positive or negative).
For example,
$ -5 $ and $ 5 $ both have an absolute value of $ 5 $, since they are five units away from zero. The absolute value of $ 11 $ is $ 11 $, representing its distance from zero. This concept helps keep our solutions accurate and consistent, especially when dealing with different types of numbers.

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91影视

Evaluate each expression. $$|15-7+3|$$

Short Answer

Step by step solution

Simplify Inside the Absolute Value

Complete the Arithmetic Operation

Apply the Absolute Value

Key Concepts

Arithmetic Operations

Simplifying Expressions

Distance from Zero

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