Question

Which inequality does NOT represent the correct comparison of two numbers on a number line?

a. 78 < −12.
b. −314 < −23
c. −9 < −6.7
d. 56 > −56

Answer 1

The incorrect inequality among the given options is 78 < -12 (Option a) because 78 is actually greater than -12, not less.

Step-by-step explanation:

The student has asked which inequality does not represent the correct comparison of two numbers on a number line. We examine each option:

• Option a: 78 < −12. This inequality is incorrect because 78 is actually greater than -12. So 78 > −12. Since 78 is a positive number and -12 is negative, the positive number is always greater on the number line.
• Option b: −314 < −23. This inequality is correct because -314 is to the left of -23 on a number line, making it smaller.
• Option c: −9 < −6.7. This is correct because -9 is to the left of -6.7 on the number line, meaning it is smaller.
• Option d: 56 > −56. This inequality is correct, as 56 is greater than -56, because positive numbers are to the right of negative numbers on the number line.

The inequality that does not correctly represent a comparison is Option a: 78 < −12.