In which of the given sets of numbers are all the numbers solutions of \( 18+2 x \geq 36 \) ? (f poirt) 9, 10, 11, 12 8.7. 6 9. 8, 7. 6 0.2 .212

To solve the inequality \( 18 + 2x \geq 36 \), we start by isolating \( x \). Subtracting 18 from both sides gives us \( 2x \geq 18 \). Dividing both sides by 2, we find that \( x \geq 9 \). Now, looking at the sets: - In the first set \( 9, 10, 11, 12 \), all numbers are greater than or equal to 9, so they are solutions. - In the second set \( 8, 7, 6 \), none of the numbers are solutions since they are all less than 9. - The third set \( 9, 8, 7, 6 \) includes 9, which is a solution, but also has numbers that are not solutions. - The fourth set \( 0.2, 0.212 \) also contains numbers less than 9, so these are not solutions. Thus, the only set where all numbers are solutions is the first one: \( 9, 10, 11, 12 \)! For a deeper look, it's fascinating that inequalities like these can model all sorts of real-life scenarios, like setting minimum height requirements for roller coasters (just like our minimum \( x \) value here). Always remember that visual aids, such as number lines, can help clarify when numbers meet or exceed specific thresholds in solutions! And if you're studying how to approach inequalities, a common mistake is to forget that if you multiply or divide both sides by a negative number, you must reverse the inequality sign. Keeping this in mind can save you from future errors and ensure you're set up for success!