Enter two values that make the inequality [tex]6 x\ \textgreater \ 24[/tex] true.
Answer (1)
The problem requires finding two values that satisfy the inequality 24"> 6 x > 24 .
Divide both sides of the inequality by 6 to isolate x , resulting in 4"> x > 4 .
Choose two values greater than 4, such as 5 and 6.
Verify that these values satisfy the original inequality.
The two values that make the inequality true are $\boxed{5, 6}.
Explanation
Understanding the Inequality We are given the inequality 24"> 6 x > 24 and we need to find two values of x that make this inequality true.
Isolating x To find the values of x , we first need to isolate x by dividing both sides of the inequality by 6. This gives us: \frac{24}{6}"> 6 6 x > 6 24 Simplifying this, we get: 4"> x > 4
Finding Valid Values Now we need to find two values of x that are greater than 4. Let's choose 5 and 6. We can check if these values satisfy the original inequality: For x = 5 : 24"> 6 ( 5 ) = 30 > 24 , which is true. For x = 6 : 24"> 6 ( 6 ) = 36 > 24 , which is true.
Final Answer Therefore, two values that make the inequality 24"> 6 x > 24 true are 5 and 6.
Examples
Imagine you are saving money, and you want to have more than $24 in your account. If you save $6 each week, this problem helps you determine how many weeks you need to save to reach your goal. By solving the inequality, you find the minimum number of weeks required to have more than $24. This concept applies to various scenarios, such as planning expenses, tracking progress toward a goal, or managing resources efficiently.
