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 4x7<54x - 7 < 5, we will isolate the variable xx. Here are the steps:

  1. Add 7 to both sides of the inequality to remove the constant term from the left side: 4x7+7<5+74x - 7 + 7 < 5 + 7 Simplifying this, we get: 4x<124x < 12

  2. Divide both sides of the inequality by 4 to solve for xx: 4x4<124\frac{4x}{4} < \frac{12}{4} Simplifying this, we get: x<3x < 3

So, the solution to the inequality 4x7<54x - 7 < 5 is x<3x < 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 4x754x - 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., 4x7>54x - 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.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Linear Equations
Basic Algebra

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9