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Chapter 2: Problem 8

Determine whether inequality is true or false. \(-8>-7\)

Short Answer

Expert verified
The inequality \(-8 > -7 \) is false.

Step by step solution

01

Understand the Inequality

The inequality given is \(-8 > -7 \). This means we need to determine if -8 is greater than -7.
02

Compare the Numbers

Place -8 and -7 on a number line. Numbers to the left are less, and numbers to the right are greater. On a number line, -8 is to the left of -7.
03

Conclusion

Since -8 is to the left of -7 on the number line, -8 is less than -7, not greater. Therefore, the inequality \(-8 > -7 \) is false.

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Key Concepts

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

number line
A number line is a straight line where every point represents a number. It helps visualize the size and order of numbers. When working with integers, positive numbers are placed to the right of zero, and negative numbers are placed to the left.
For example, consider the numbers -8 and -7. On the number line, -8 is placed to the left of -7. This layout makes comparing numbers more straightforward. In general, the further left a number is on the number line, the smaller it is. Conversely, the further right a number is, the larger it is.
comparing integers
Comparing integers means determining which of two numbers is larger or smaller. With positive numbers, this can be done quickly, but negative numbers can be more tricky.
Let's compare -8 and -7:
  • -8 is farther to the left on the number line than -7.
  • Among negative numbers, the number closer to zero is always greater. Hence, -7 is greater than -8.
  • Remember, the further left, the smaller the number.
false inequality
A false inequality is simply an inequality statement that isn't true. For example, take -8 > -7. This statement implies that -8 is greater than -7.
Looking at a number line, it is clear that -8 is to the left of -7, making it smaller, not larger.
  • Understanding the layout of numbers helps identify whether an inequality is true or false.
  • Practicing with number lines can sharpen your skills in spotting false inequalities.

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