Problem 73 Translate the following into a m... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 1: Problem 73

Translate the following into a mathematical statement. Negative seven is less than zero.

Short Answer

Expert verified

-7 < 0

Step by step solution

Translate Each Part

Start by identifying each part of the statement. 'Negative seven' refers to the number -7. 'Less than' is the mathematical operation for inequality (<). 'Zero' simply refers to 0.

Construct the Mathematical Statement

Combine the translated parts into a mathematical statement. This means representing 'Negative seven' as -7, 'is less than' as <, and 'zero' as 0, creating the inequality -7 < 0.

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Key Concepts

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

Understanding Inequality Symbols

Inequality symbols are fundamental components in mathematics used to compare values. When working with inequalities, you will encounter symbols such as:

$<$ means "less than".
$>$ means "greater than".
$\leq$ means "less than or equal to".
$\geq$ means "greater than or equal to".

These symbols help in forming mathematical statements that describe the relationship between numbers. In our exercise, the phrase "negative seven is less than zero" uses the symbol $<$ to show that negative seven is smaller than zero. This is because negative numbers are always less than positive numbers. Inequality symbols act like direction markers in math, guiding us on how one value compares to another.

Handling Negative Numbers

Negative numbers can sometimes be tricky to understand. They are numbers less than zero, represented with a minus sign $-$ in front of them. The more negative a number, the smaller it is. For instance, $-7$ is smaller than $-3$, because $-7$ is farther away from zero.

Negative numbers are often used in contexts like temperatures below freezing or financial loss.
In math, when you see a minus sign in front of a number, it indicates a number below zero.

In our specific exercise, "negative seven" is written as $-7$. It's important to remember that the value of any negative number decreases as the numeral gets larger, making it smaller in comparison to less negative or positive numbers. Recognizing how these values interact helps us accurately interpret and solve problems with negative numbers.

Implementing Step-by-Step Solutions

Using a step-by-step approach is a great way to simplify complex mathematical expressions and ensure you understand each component thoroughly.
Here鈥檚 why it鈥檚 beneficial:

It allows you to break down problems into smaller, manageable parts.
Ensures each segment is understood before going on to the next.
Helps prevent mistakes from misunderstanding or overlooking crucial steps.

In the "negative seven is less than zero" exercise, starting with translating parts of a statement was crucial:

Identify each part: "negative seven" as $-7$, "less than" as $<$, and "zero" as $0$.
Combine these parts to form the inequality $-7 < 0$.

Practicing this methodical process not only improves accuracy but also builds confidence in solving varied and more complex mathematical tasks effectively.

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91影视

Translate the following into a mathematical statement. Negative seven is less than zero.

Short Answer

Step by step solution

Translate Each Part

Construct the Mathematical Statement

Key Concepts

Understanding Inequality Symbols

Handling Negative Numbers

Implementing Step-by-Step Solutions

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