Math Problem Statement
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.
Solution
To solve the inequality , we will isolate the variable . Here are the steps:
-
Add 7 to both sides of the inequality to remove the constant term from the left side: Simplifying this, we get:
-
Divide both sides of the inequality by 4 to solve for : Simplifying this, we get:
So, the solution to the inequality is .
Would you like more details on any of these steps or have any questions?
Here are some related questions you might find interesting:
- How would you solve the inequality if it was ?
- What are some common mistakes when solving linear inequalities?
- How does the solution change if the inequality is reversed (e.g., )?
- Can you solve and graph the inequality on a number line?
- 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.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Linear Equations
Basic Algebra
Formulas
-
Theorems
-
Suitable Grade Level
Grades 7-9