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To solve the inequality \(4x - 7 < 5\), we will isolate the variable \(x\). Here are the steps:

1. **Add 7 to both sides** of the inequality to remove the constant term from the left side:
   \[
   4x - 7 + 7 < 5 + 7
   \]
   Simplifying this, we get:
   \[
   4x < 12
   \]

2. **Divide both sides** of the inequality by 4 to solve for \(x\):
   \[
   \frac{4x}{4} < \frac{12}{4}
   \]
   Simplifying this, we get:
   \[
   x < 3
   \]

So, the solution to the inequality \(4x - 7 < 5\) is \(x < 3\).

Would you like more details on any of these steps or have any questions?

Here are some related questions you might find interesting:
1. How would you solve the inequality if it was \(4x - 7 \leq 5\)?
2. What are some common mistakes when solving linear inequalities?
3. How does the solution change if the inequality is reversed (e.g., \(4x - 7 > 5\))?
4. Can you solve and graph the inequality on a number line?
5. What is the difference between solving equations and solving inequalities?

**Tip:** When solving inequalities, remember that if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

The query submitted by the user: To solve the inequality \(4x - 7 < 5\), we will isolate the variable \(x\). Here are the steps:

1. **Add 7 to both sides** of the inequality to remove the constant term from the left side:
   \[
   4x - 7 + 7 < 5 + 7
   \]
   Simplifying this, we get:
   \[
   4x < 12
   \]

2. **Divide both sides** of the inequality by 4 to solve for \(x\):
   \[
   \frac{4x}{4} < \frac{12}{4}
   \]
   Simplifying this, we get:
   \[
   x < 3
   \]

So, the solution to the inequality \(4x - 7 < 5\) is \(x < 3\).

Would you like more details on any of these steps or have any questions?

Here are some related questions you might find interesting:
1. How would you solve the inequality if it was \(4x - 7 \leq 5\)?
2. What are some common mistakes when solving linear inequalities?
3. How does the solution change if the inequality is reversed (e.g., \(4x - 7 > 5\))?
4. Can you solve and graph the inequality on a number line?
5. What is the difference between solving equations and solving inequalities?

**Tip:** When solving inequalities, remember that if you multiply or divide both sides by a negative number, you must reverse the inequality sign.

Learn how to solve the inequality 4x - 7 < 5 step-by-step with detailed explanations. This problem covers key algebraic concepts, including inequalities and basic algebra. Suitable for students in Grades 7-9.

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