What is the solution to this inequality?

$-16 x>-80$

A. $x<-5$
B. $x<5$
C. $x>5$
D. $x>-5$

Divide both sides of the inequality by -16.
Remember to reverse the inequality sign when dividing by a negative number.
Simplify the resulting inequality.
The solution to the inequality is x < 5 ​ .

Explanation

Understanding the Inequality We are given the inequality -80"> − 16 x > − 80 . Our goal is to isolate x to find the solution.

Dividing by a Negative Number To isolate x , we need to divide both sides of the inequality by − 16 . Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.

Performing the Division Dividing both sides by − 16 , we get: − 16 − 16 x ​ < − 16 − 80 ​

Simplifying the Result Simplifying the fractions, we have: x < 5

Final Answer Therefore, the solution to the inequality is x < 5 .


Examples
Imagine you're sharing a pizza with friends. If the pizza has a certain number of slices and you want to make sure everyone gets at least a certain amount, you can use inequalities to figure out how many friends you can invite. For example, if you have 16 slices and want each person to have more than 2 slices, the inequality would be 2"> x 16 ​ > 2 , where x is the number of people. Solving this inequality helps you determine the maximum number of friends you can invite while ensuring everyone gets enough pizza. Inequalities are useful for resource allocation, setting limits, and making sure conditions are met in various real-life scenarios.

Answered by GinnyAnswer | 2025-07-06