Problem 105 Translate to an inequality. Th... [FREE SOLUTION]

Chapter 1: Problem 105

Translate to an inequality. The distance from \(x\) to 0 is no more than \(10 .\)

Short Answer

Expert verified

The inequality is \(|x| \leq 10\).

Step by step solution

Understanding the concept of distance

The distance from a number to 0 on a number line is represented by the absolute value of that number. So, the distance from a number x to 0 is \(|x|\).

Translating the word problem into a mathematical inequality

The problem states that the distance from x to 0 is no more than 10. This implies that the absolute value \(|x|\) should be less than or equal to 10. Therefore, the inequality representing this condition is: \(|x| \leq 10\).

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Key Concepts

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

absolute value

The concept of absolute value is crucial when dealing with distances on the number line. Absolute value represents the distance of a number from zero without considering direction. It is always a non-negative number. For example, the absolute value of both -5 and 5 is 5 because both points are 5 units away from zero on a number line. We denote absolute value using vertical bars. So, the absolute value of any number x is written as \(|x|\). This is a foundational concept in mathematics because it helps us understand and calculate distances between numbers, regardless of their positions or signs.

number line

A number line is a visual representation of numbers on a straight, horizontal line. Each point on the line corresponds to a real number. In the context of inequalities and absolute values, the number line helps to illustrate the position and distance of numbers from zero. To represent numbers, we typically draw a horizontal line and mark a point halfway called zero. From there, positive numbers are marked to the right, and negative numbers to the left. The number line provides a clear visual tool for understanding how far any number is from zero or any other number.

mathematical translation

Mathematical translation involves converting statements or word problems into mathematical expressions or equations. In the context of our exercise, it means interpreting the phrase 'the distance from x to 0 is no more than 10' and expressing it using mathematical symbols. This requires understanding that 'distance' translates to absolute value and 'no more than' translates to 'less than or equal to' (鈮�). Hence, 'the distance from x to 0 is no more than 10' translates to \(|x| \leq 10\). Being able to translate words into mathematical symbols requires familiarity with the specific language of mathematics, which is a vital skill to develop for solving word problems effectively.

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91影视

Translate to an inequality. The distance from \(x\) to 0 is no more than \(10 .\)

Short Answer

Step by step solution

Understanding the concept of distance

Translating the word problem into a mathematical inequality

Key Concepts

absolute value

number line

mathematical translation

One App. One Place for Learning.

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