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4) You decided whether a number is a solution of an inequality. Which of these numbers is a solution of the inequality \( 3 x \geq 18 \) ?

Ask by Reid Garza. in the United States
Feb 03,2025

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Tutor-Verified Answer

Answer

Any number greater than or equal to 6 is a solution to the inequality \( 3x \geq 18 \).

Solution

To determine which numbers are solutions to the inequality \( 3x \geq 18 \), we will first solve the inequality for \( x \). ### Step 1: Solve the inequality We start with the inequality: \[ 3x \geq 18 \] To isolate \( x \), we divide both sides of the inequality by 3: \[ x \geq \frac{18}{3} \] ### Step 2: Simplify the right side Calculating the right side gives: \[ x \geq 6 \] ### Conclusion The solution to the inequality \( 3x \geq 18 \) is \( x \geq 6 \). ### Step 3: Identify solutions Any number that is greater than or equal to 6 is a solution to the inequality. For example, numbers like 6, 7, 8, etc., are solutions, while numbers like 5, 4, 3, etc., are not. If you have specific numbers to check, please provide them, and I can confirm whether they are solutions to the inequality.

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Bonus Knowledge

To determine if a number is a solution to the inequality \( 3x \geq 18 \), first solve for \( x \) by dividing both sides by 3. This gives us \( x \geq 6 \). Any number equal to or greater than 6 will satisfy the inequality. So, for example, 6, 7, or even 10 would all be valid solutions! Now, don't get stuck! A common mistake is to misinterpret the inequality's direction. Always remember, if you multiply or divide by a negative number, the inequality sign flips! So keep your eyes on the prize and check your steps!

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