What is the solution to this inequality?
[tex]x-7\ \textgreater \ -6[/tex]
A. [tex]x\ \textless \ -13[/tex]
B. [tex]x\ \textless \ 1[/tex]
C. [tex]x\ \textgreater \ 1[/tex]
D. [tex]x\ \textgreater \ -13[/tex]
Answer (1)
Add 7 to both sides of the inequality: -6 + 7"> x − 7 + 7 > − 6 + 7 .
Simplify the inequality: 1"> x > 1 .
The solution to the inequality is 1"> x > 1 .
Therefore, the solution is 1}"> x > 1 .
Explanation
Understanding the Inequality We are given the inequality -6"> x − 7 > − 6 . Our goal is to isolate x on one side of the inequality to find the solution.
Adding 7 to Both Sides To isolate x , we need to add 7 to both sides of the inequality. This will cancel out the -7 on the left side:
-6 + 7"> x − 7 + 7 > − 6 + 7
Simplifying the Inequality Now, simplify both sides of the inequality:
1"> x > 1
Stating the Solution The solution to the inequality is 1"> x > 1 . This means that any value of x greater than 1 will satisfy the original inequality.
Examples
Imagine you're saving money for a new video game that costs $7. You already have some money, but you need to have more than 6 t o b u y t h e g am e . T h e in e q u a l i t y x - 7 > -6 re p rese n t s t hi ss i t u a t i o n , w h ere x$ is the amount of money you have. Solving the inequality tells you that you need to have more than $1 to be able to afford the game after buying it.
