Question
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Answer
The solution to the inequality is \( n \geq -1 \).
Solution
We start with the inequality:
-22 - n ≤ -21
Step 1: Add 22 to both sides to isolate -n.
-22 - n + 22 ≤ -21 + 22
-n ≤ 1
Step 2: Multiply both sides by -1, remembering to reverse the inequality sign:
n ≥ -1
Thus, the solution to the inequality is:
n ≥ -1
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Simplify this solution Beyond the Answer
To solve the inequality \( -22 - n \leq -21 \), we can start by adding 22 to both sides. This will help us isolate the term with \( n \). So, we have: \[ -n \leq -21 + 22 \] \[ -n \leq 1 \] Next, let's multiply the entire inequality by -1 to solve for \( n \). Remember, multiplying by a negative number reverses the inequality sign: \[ n \geq -1 \] Now, we have our solution: \( n \) must be greater than or equal to \(-1\). So, in interval notation, the solution is \( n \in [-1, \infty) \). This means \( n \) can take any value starting from \(-1\) and going upwards!
