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Chapter 2: Problem 10

Determine whether inequality is true or false. \(-6 \geq-8\)

Short Answer

Expert verified
The inequality \(-6 \biggeq -8\) is true.

Step by step solution

01

Understand the inequality symbols

The symbol \(\biggeq\) means 'greater than or equal to.' Hence, \(-6 \biggeq -8\) states that \(-6\) is greater than or equal to \(-8\).
02

Compare the two numbers

When comparing two negative numbers, the one closer to zero is larger. In this case, \(-6\) is closer to zero than \(-8\), making \(-6\) larger than \(-8\).
03

Conclusion

Since \(-6\) is indeed greater than \(-8\), the inequality \(-6 \biggeq -8\) is true.

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Key Concepts

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

inequality symbols
An inequality is a mathematical statement that compares two values, showing if one is larger, smaller, or equal to the other. Common inequality symbols include:
  • \(\biglt\) means 'less than'
  • \(\biggt\) means 'greater than'
  • \(\bigeq\) means 'equal to'
  • \(\bigleq\) means 'less than or equal to'
  • \(\biggeq\) means 'greater than or equal to'

In the exercise, the symbol \(\biggeq\) (greater than or equal to) is used. This means we compare if the first value is either greater than or the same as the second value. Understanding these symbols is crucial when working with inequalities.
comparing negative numbers
Negative numbers can be tricky to compare because they work differently than positive numbers. The closer a number is to zero, the larger it is.
For example, between -6 and -8, -6 is closer to zero. This makes -6 larger than -8.
Think of negative numbers as debts: owing less money (closer to zero) is better than owing more money (further from zero). So, -6 is a better (or larger) debt compared to -8. This helps us understand the true magnitude of negative values.
algebraic expressions
Algebraic expressions are combinations of numbers, variables, and operations (like addition, subtraction, multiplication, and division). Unlike simple numbers, they can represent complex quantities or values that change.
In the context of inequalities, we often compare these expressions to see which is larger or smaller, or if they are equal.
For example, if you have \(x + 3 \biggeq y - 2\) and know the specific values of x and y, you can replace x and y to make the comparison. Understanding how to manipulate and compare these expressions is key to solving algebra problems.

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