To solve the inequality \( 2x + 5 < 3x + 4 \), let's break it down step-by-step:

### Step 1: Isolate the variable
1. Subtract \( 2x \) from both sides to get all \( x \)-terms on one side:
   \[
   2x + 5 - 2x < 3x + 4 - 2x
   \]
   Simplifying this gives:
   \[
   5 < x + 4
   \]

### Step 2: Isolate \( x \)
2. Subtract 4 from both sides to isolate \( x \):
   \[
   5 - 4 < x + 4 - 4
   \]
   Simplifying this gives:
   \[
   1 < x
   \]

### Step 3: Rewrite the inequality
The solution can be written as:
   \[
   x > 1
   \]

### Final Answer
The solution to the inequality is:
\[
x > 1
\]

Would you like further details or have any questions?

### 5 Related Questions
1. How would the solution change if the inequality were \( 2x + 5 > 3x + 4 \)?
2. What happens if you change the inequality to \( 2x + 5 \leq 3x + 4 \)?
3. Can you solve \( 4x - 7 < 2x + 9 \) in a similar way?
4. How would you graph the solution \( x > 1 \) on a number line?
5. How do you handle inequalities when multiplying or dividing by a negative number?

### Tip
When solving inequalities, if you multiply or divide both sides by a negative number, you must **flip the direction** of the inequality sign!

Discover how to solve the linear inequality 2x + 5 < 3x + 4 with a clear step-by-step guide. This problem teaches algebraic concepts such as isolating the variable and simplifying inequalities, ideal for students in Grades 6-8.

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