The inequality symbol to compare
and
is ![\boxed{ - 26 < 54}.](https://tex.z-dn.net/?f=%5Cboxed%7B%20-%2026%20%3C%2054%7D.)
Further explanation:
Given:
The inequality equation is ![- 3 + 7\underline {\,\,\,\,\,} - 10 - 2](https://tex.z-dn.net/?f=-%203%20%2B%207%5Cunderline%20%7B%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%7D%20%20-%2010%20-%202)
The options are as follows,
A. ![=](https://tex.z-dn.net/?f=%3D)
B. ![](https://tex.z-dn.net/?f=%3C)
C. ![>](https://tex.z-dn.net/?f=%3E)
D. ![\leqslant](https://tex.z-dn.net/?f=%5Cleqslant)
Explanation:
The inequality equation is ![- 3 + 7\underline {\,\,\,\,\,} - 10 – 2.](https://tex.z-dn.net/?f=-%203%20%2B%207%5Cunderline%20%7B%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%7D%20%20-%2010%20%E2%80%93%202.)
First solve the left hand side of the inequality equation.
![\begin{aligned}A &= - 3 + 7\\&= 4\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%20%26%3D%20-%203%20%2B%207%5C%5C%26%3D%204%5C%5C%5Cend%7Baligned%7D)
Now solve the right hand of the inequality equation.
![\begin{aligned}B&= - 10 - 2\\&= - 12\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DB%26%3D%20-%2010%20-%202%5C%5C%26%3D%20-%2012%5C%5C%5Cend%7Baligned%7D)
is a positive number and
is a negative number. Positive numbers are always greater than the negative numbers. Therefore, 4is greater than
.
Negative numbers are on the left of zero and positive numbers are on right of zero.
is on the left side of the number line and 4 is on the right on the number line.
Therefore, the inequality symbol is ![](https://tex.z-dn.net/?f=%3C.)
The inequality symbol to compare
and
is ![\boxed{ - 26 < 54}.](https://tex.z-dn.net/?f=%5Cboxed%7B%20-%2026%20%3C%2054%7D.)
Option A is not correct.
Option B is not correct.
Option C is correct.
Option D is not correct.
Kindly refer to the image attached below.
Learn more:
- Learn more about inverse of the function brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: in equality, inequality symbol, greater than, less than, -26, 54, =, numbers, real numbers, negative numbers, positive numbers, compare, whole number natural number, number line, left of zero, right of zero.