Solve the inequality: $-2 x>-6$

A. $x>-3$
B. $x<3$
C. $x<-3$
D. $x>3$

Divide both sides of the inequality -6"> − 2 x > − 6 by − 2 .
Remember to reverse the inequality sign when dividing by a negative number.
Simplify the inequality to find x < 3 .
The solution to the inequality is x < 3 ​ .

Explanation

Analyze the inequality We are given the inequality -6"> − 2 x > − 6 . Our goal is to isolate x to find the solution.

Divide by -2 and flip the inequality sign To isolate x , we need to divide both sides of the inequality by − 2 . It's very important to remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign.

Perform the division Dividing both sides by − 2 , we get: − 2 − 2 x ​ < − 2 − 6 ​

Simplify the result Simplifying the fractions, we have: x < 3

State the solution Therefore, the solution to the inequality -6"> − 2 x > − 6 is x < 3 .


Examples
Imagine you're sharing cookies with a friend, but you owe them some from the last time. If -6"> − 2 x > − 6 represents the debt (where x is the number of cookies), solving the inequality tells you how many cookies you need to give back to have fewer than 0 cookies owed (i.e., to be in the clear). This concept applies to budgeting, resource allocation, and understanding constraints in everyday situations.

Answered by GinnyAnswer | 2025-07-07