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\( -10 n<-50 \) or \( n+4 \leq 2 \)

Ask by Cummings Mitchell. in the United States
Feb 20,2025

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Answer

The solutions are \( n > 5 \) or \( n \leq -2 \).

Solution

Solve the equation \( -10n<-50 \). Solve the inequality by following steps: - step0: Solve for \(n\): \(-10n<-50\) - step1: Change the signs: \(10n>50\) - step2: Divide both sides: \(\frac{10n}{10}>\frac{50}{10}\) - step3: Divide the numbers: \(n>5\) Solve the equation \( n+4 \leq 2 \). Solve the inequality by following steps: - step0: Solve for \(n\): \(n+4\leq 2\) - step1: Move the constant to the right side: \(n\leq 2-4\) - step2: Subtract the numbers: \(n\leq -2\) The solutions to the given inequalities are: 1. \( n > 5 \) 2. \( n \leq -2 \)

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The Deep Dive

To solve the first inequality \( -10n < -50 \), you would divide both sides by -10, which flips the inequality sign to get \( n > 5 \). For the second inequality \( n + 4 \leq 2 \), subtracting 4 from both sides gives \( n \leq -2 \). So your final solution is \( n > 5 \) or \( n \leq -2 \), meaning n can be any number greater than 5 or less than or equal to -2! If you want to illustrate this solution visually, consider drawing a number line. Mark the point 5 with an open circle (because it's greater than, not equal) and shade all numbers greater than that. Then mark -2 with a filled circle (indicating it is included) and shade all numbers less than that. This way, you create a clear picture of all possible values for \( n \)!

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