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Chapter 1: Problem 52

Simplify. $$ |10(-5)|+1(-1) $$

Short Answer

Expert verified
49

Step by step solution

01

Evaluate Inside the Absolute Value

First, calculate the expression inside the absolute value. \[ 10(-5) = -50 \]
02

Apply the Absolute Value

Next, apply the absolute value to the result from Step 1. \[ |-50| = 50 \]
03

Evaluate the Multiplication Outside the Absolute Value

Calculate the multiplication outside the absolute value \[ 1(-1) = -1 \]
04

Add the Results

Finally, add the results from Steps 2 and 3 together. \[ 50 + (-1) = 49 \]

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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 is a measure of its distance from zero on the number line, regardless of direction. It is always a non-negative number. When we have an expression like \(|10(-5)|\), we first need to perform the multiplication inside the absolute value. This transformation of inner expressions is crucial before applying the absolute value.

Here, multiplying 10 by -5 gives us -50. Once we have this result, we take the absolute value of -50, which is 50. The notation \( |x| \) denotes absolute value, which can be understood by considering it as a 'positive distance' from zero.
Multiplication
Multiplication in algebra is the process of combining numbers to get a new value, called the product. It can involve both positive and negative numbers.
When multiplying a positive number with a negative number, the product is negative, as seen in the expression 10(-5) = -50.

In combination with absolute value calculations, this step is crucial because it sets the stage for understanding whether the product inside will remain negative or turn positive when we apply the absolute value. After computing \(10(-5) = -50\), we proceed by using the absolute value to get 50.
Addition
Addition is a basic mathematical operation, and in algebra, you will often add numbers or expressions together. After simplifying parts of an equation separately, you will need to add the results.
In this problem, after evaluating \(|10(-5)|\) to get 50 and \(1(-1)\) to get -1, we perform the final addition.

Adding 50 and -1, we get 49. Remember, when adding a positive and negative number, think of it as subtracting the negative number's absolute value from the positive number. Therefore, \(50 + (-1) = 49\).

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Most popular questions from this chapter

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