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!