Use an inequality symbol $(<,>,-,\leq,\geq)$ to compare $-3+7$ and $-10-2$.
Answer (1)
Evaluate the left expression: − 3 + 7 = 4 .
Evaluate the right expression: − 10 − 2 = − 12 .
Compare the two results: -12"> 4 > − 12 .
Therefore, -10-2"> − 3 + 7 > − 10 − 2 . }"> >
Explanation
Understanding the problem We are asked to compare two numerical expressions: − 3 + 7 and − 10 − 2 using an inequality symbol. The possible inequality symbols are , ="> < , > , = or ≤ .
Evaluating the left expression First, let's evaluate the expression on the left: − 3 + 7 . When we add − 3 and 7 , we get 4 .
Evaluating the right expression Next, let's evaluate the expression on the right: − 10 − 2 . When we subtract 2 from − 10 , we get − 12 .
Comparing the expressions Now, we compare the two results: 4 and − 12 . Since 4 is greater than − 12 , we use the "> > symbol. Therefore, -10-2"> − 3 + 7 > − 10 − 2 .
Examples
In everyday life, comparing numerical expressions with inequality symbols helps us understand relative quantities. For example, if you have $4 and your friend has a debt of 12 ( -12), you have more money than your friend. This concept is also used in budgeting, where you compare your income and expenses to determine if you have a surplus or a deficit.
