What is the solution to this inequality?
$x-6<-4$
A. $x<2$
B. $x<-10$
C. $x>-10$
D. $x>2$
Answer (1)
Add 6 to both sides of the inequality: x − 6 + 6 < − 4 + 6 .
Simplify the inequality: x < 2 .
The solution to the inequality is x < 2 .
The correct answer is x < 2 .
Explanation
Understanding the Problem We are given the inequality x − 6 < − 4 and asked to find the solution.
Isolating x To solve the inequality, we need to isolate x on one side. We can do this by adding 6 to both sides of the inequality: x − 6 + 6 < − 4 + 6
Simplifying the Inequality Simplifying both sides, we get: x < 2
Final Answer The solution to the inequality is x < 2 . Therefore, the correct answer is A.
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, if you're budgeting your expenses, you might use an inequality to determine how much you can spend on entertainment each month while still covering your essential bills. If your monthly income is I and your essential expenses are E , then the amount you can spend on entertainment, S , must satisfy the inequality S ≤ I − E . Solving this inequality helps you manage your finances effectively.
