Solve the following inequality for n*n*. Write your answer in simplest form.

minus, 5, n, plus, 8, is less than, minus, 3, n, plus, 4

−5*n*+8<

−3*n*+4

Let's solve the inequality \( -5n + 8 < -3n + 4 \) for \( n \).

1. First, we'll add \( 5n \) to both sides to get the terms involving \( n \) on one side:
   \[
   -5n + 8 + 5n < -3n + 4 + 5n
   \]
   Simplifying this, we get:
   \[
   8 < 2n + 4
   \]

2. Next, we'll subtract 4 from both sides to isolate the term with \( n \):
   \[
   8 - 4 < 2n + 4 - 4
   \]
   Simplifying this, we obtain:
   \[
   4 < 2n
   \]

3. Finally, we'll divide both sides by 2 to solve for \( n \):
   \[
   \frac{4}{2} < \frac{2n}{2}
   \]
   Simplifying this, we get:
   \[
   2 < n
   \]
   or equivalently,
   \[
   n > 2
   \]

So, the solution in simplest form is \( n > 2 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you solve a similar inequality, such as \( -7n + 6 < -4n + 9 \)?
2. What happens if the inequality sign is reversed, like \( -5n + 8 > -3n + 4 \)?
3. How can you represent the solution \( n > 2 \) on a number line?
4. What changes if the inequality involves a negative coefficient after isolating \( n \), like \( -2n < 4 \)?
5. How do you solve the inequality if the terms were \( -5n + 8 \leq -3n + 4 \)?

**Tip:** Be careful with the sign when adding or subtracting terms during the process of solving inequalities.

Learn how to solve the inequality -5n + 8 < -3n + 4 step-by-step with a detailed solution. This problem involves basic algebraic concepts like solving linear inequalities. Suitable for students in Grades 7-9.

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