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Which of the following is a solution to the inequality below? \[ 9 \leq 11-\frac{g}{7} \] \( g=21 \) \( g=49 \) \( g=14 \)

Ask by Chang Marshall. in the United States
Mar 09,2025

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Answer

\( g = 14 \) is the solution to the inequality.

Solution

1. Start with the inequality: \[ 9 \leq 11 - \frac{g}{7} \] 2. Subtract \( 11 \) from both sides: \[ 9 - 11 \leq 11 - \frac{g}{7} - 11 \] \[ -2 \leq - \frac{g}{7} \] 3. Multiply both sides by \(-1\) (remember to flip the inequality sign when multiplying by a negative number): \[ 2 \geq \frac{g}{7} \] 4. Multiply both sides by \( 7 \) to solve for \( g \): \[ 2 \times 7 \geq g \] \[ 14 \geq g \] This means: \[ g \leq 14 \] 5. Check the given options: - \( g = 21 \) does not satisfy \( 21 \leq 14 \). - \( g = 49 \) does not satisfy \( 49 \leq 14 \). - \( g = 14 \) satisfies \( 14 \leq 14 \). Therefore, the solution is \( g = 14 \).

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Beyond the Answer

To solve the inequality \( 9 \leq 11-\frac{g}{7} \), we can start by isolating \( g \). Subtracting 11 from both sides gives us \( -2 \leq -\frac{g}{7} \). Multiplying by -1 (which flips the inequality sign) results in \( 2 \geq \frac{g}{7} \). Then, multiplying both sides by 7 leads us to \( 14 \geq g \) or \( g \leq 14 \). Now, if we check the provided values: - For \( g = 21 \): Not a solution (21 > 14) - For \( g = 49 \): Not a solution (49 > 14) - For \( g = 14 \): This is a solution (14 = 14) Therefore, the solution to the inequality is \( g = 14 \). Now, keep that calculator handy! It's easy to make simple calculation mistakes if you're not careful. Double-check your operations at each step, especially when multiplying, as flipping signs can often lead to errors in inequalities. Another common mistake is misinterpreting the direction of the inequality when multiplying or dividing by negative numbers—remember, doing that flips it! If you're interested in mastering inequalities further, consider practicing some online math platforms or apps. They often have interactive problems and instant feedback, making learning engaging and fun. Additionally, you could check out "The Art of Problem Solving" series for a deeper dive into mathematical reasoning through challenging and creative problems!

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