(n / 9) + 4 < 3
Understand the Problem
The question is asking to solve the inequality involving the variable n. Specifically, we need to isolate n in the inequality (n/9) + 4 < 3 and determine the solution set.
Answer
The solution is $n < -9$, or in interval notation, $(-\infty, -9)$.
Answer for screen readers
The solution to the inequality is $n < -9$, or in interval notation, $(-\infty, -9)$.
Steps to Solve
- Subtract 4 from both sides
To isolate the term with $n$, subtract 4 from both sides of the inequality:
$$(\frac{n}{9}) + 4 - 4 < 3 - 4$$
This simplifies to:
$$\frac{n}{9} < -1$$
- Multiply both sides by 9
Next, to eliminate the fraction, multiply both sides of the inequality by 9. Remember, since 9 is positive, the direction of the inequality remains the same:
$$9 \cdot \frac{n}{9} < 9 \cdot (-1)$$
This simplifies to:
$$n < -9$$
- Determine the solution set
The solution set indicates the values of $n$ that satisfy the inequality. Since $n$ must be less than -9, we can express the solution set in interval notation:
$$(-\infty, -9)$$
The solution to the inequality is $n < -9$, or in interval notation, $(-\infty, -9)$.
More Information
Inequalities represent a range of values, and the solution $(-\infty, -9)$ means that any number less than -9 will satisfy the inequality. This is useful in fields like algebra and calculus where understanding ranges is key.
Tips
- Not reversing the inequality sign when multiplying or dividing by a negative number (though this problem does not involve such a case).
- Forgetting to perform the same operation on both sides of the inequality.
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