Question
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Answer
n ≤ -3
Solution
To solve the inequality 2n ≤ -6, follow these steps:
1. Start with the inequality:
2n ≤ -6
2. Divide both sides of the inequality by 2 (since 2 is positive, the inequality sign remains unchanged):
n ≤ -6/2
3. Simplify the division:
n ≤ -3
Thus, the solution to the inequality is n ≤ -3.
This means that any number less than or equal to -3 will satisfy the inequality 2n ≤ -6.
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Simplify this solution The Deep Dive
To solve the inequality \( 2n \leq -6 \), start by isolating \( n \). Divide both sides by 2, which gives you \( n \leq -3 \). This means that any value of \( n \) that is less than or equal to -3 satisfies the inequality. So, \( n \) could be -3, -4, -5, and so on! Inequalities like this one can be visualized on a number line. You would shade all the numbers to the left of -3, including -3 itself, to indicate all possible solutions. It's a great way to see at a glance which numbers work and which don’t!
