An inequality is shown.
[tex]12(x-2) \ \textless \ 24[/tex]
Which of the following is the solution to the inequality?
A. [tex]x\ \textless \ 0[/tex]
B. [tex]x\ \textgreater \ 0[/tex]
C. [tex]x\ \textless \ 12[/tex]
D. [tex]x\ \textless \ 4[/tex]
Answer (2)
Divide both sides of the inequality by 12: x − 2 < 2 .
Add 2 to both sides of the inequality: x < 4 .
The solution to the inequality is x < 4 .
The correct answer is D. x < 4
Explanation
Understanding the Problem We are given the inequality 12 ( x − 2 ) < 24 and we need to find the solution among the given options.
Simplifying the Inequality First, we divide both sides of the inequality by 12 to simplify it: 12 12 ( x − 2 ) < 12 24 x − 2 < 2
Isolating x Next, we add 2 to both sides of the inequality to isolate x: x − 2 + 2 < 2 + 2 x < 4
Finding the Solution Therefore, the solution to the inequality is x < 4 . Comparing this to the given options, we see that option D is the correct answer.
Examples
Understanding inequalities is crucial in many real-world scenarios. For example, imagine you're planning a road trip and have a budget constraint. If you know your car's fuel efficiency and the price of gas, you can use inequalities to determine how far you can travel without exceeding your budget. Similarly, in business, inequalities can help determine the minimum sales needed to make a profit or the maximum expenses allowed to stay within a certain budget.
The solution to the inequality 12 ( x − 2 ) < 24 is x < 4 . Therefore, the correct answer is option D. x < 4 .
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