Solve the following inequality for nn. Write your answer in simplest form.
5, n, plus, 5, is greater than, 6, n, minus, 9
5n+5>
6n−9

Let's solve the inequality \( 5n + 5 > 6n - 9 \).

1. First, we'll subtract \( 5n \) from both sides to get the terms involving \( n \) on one side:
   \[
   5n + 5 - 5n > 6n - 9 - 5n
   \]
   Simplifying this, we get:
   \[
   5 > n - 9
   \]

2. Next, we'll add 9 to both sides to isolate \( n \):
   \[
   5 + 9 > n - 9 + 9
   \]
   Simplifying this, we obtain:
   \[
   14 > n
   \]

3. The solution can be written as:
   \[
   n < 14
   \]

So, the solution in simplest form is \( n < 14 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you solve a similar inequality with more variables, like \( 7n + 3 > 2n + 8 \)?
2. What changes if the inequality is \( 5n + 5 \geq 6n - 9 \)?
3. How do you graph the solution \( n < 14 \) on a number line?
4. Can you solve the inequality if the terms were \( 5n + 5 \leq 6n - 9 \)?
5. What if the inequality involved fractions, like \( \frac{5n}{3} + 5 > \frac{6n}{4} - 9 \)?

**Tip:** Always isolate the variable on one side of the inequality to simplify solving the problem.

Learn how to solve the inequality 5n + 5 > 6n - 9 with a detailed step-by-step solution. This problem involves solving linear inequalities, isolating variables, and interpreting inequality solutions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation