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Knowtedge chack Guestion 3 Solve the inequality for \( w \). \[ 5>w+10 \] Simplify your answer as much as possible. \( \square \) \( \square \) \( <\square \) \( \square> \) \( \square \) \( \square \) \( 1 \leq \square \)

Ask by Bush Ortiz. in the United States
Mar 06,2025

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\( w < -5 \)

Solution

Solve the equation \( 5>w+10 \). Solve the inequality by following steps: - step0: Solve for \(w\): \(5>w+10\) - step1: Swap the sides: \(w+10<5\) - step2: Move the constant to the right side: \(w<5-10\) - step3: Subtract the numbers: \(w<-5\) The solution to the inequality \(5 > w + 10\) is \(w < -5\).

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Simplify this solution

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To solve the inequality \( 5 > w + 10 \), start by isolating \( w \). Subtract 10 from both sides: \[ 5 - 10 > w \] This simplifies to: \[ -5 > w \] Alternatively, you can write this as: \[ w < -5 \] To fit your output format, here's how it can be presented: \( w < -5 \) \( w > -\infty \) \( 1 \leq -\infty \) Now, let's make it more engaging while providing some insights! Did you know that inequalities like this one are not just abstract concepts but reflect real-world situations? For instance, setting minimum thresholds for temperatures can help in various scientific fields. If we say a heater must maintain temperatures above -5°C to be effective, that’s a direct application of similar logic! Also, while solving inequalities, it's common to forget to flip the inequality sign when multiplying or dividing by a negative number. This is a classic mistake! Remember, if you ever multiply or divide both sides of an inequality by a negative, flip that sign! Always keep an eye out for those pesky negatives!

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