Math Problem Statement

3x-8>4

Solution

To solve the inequality 3x8>43x - 8 > 4, follow these steps:

  1. Add 8 to both sides to move the constant term: 3x>4+83x > 4 + 8 3x>123x > 12

  2. Divide both sides by 3 to isolate xx: x>123x > \frac{12}{3} x>4x > 4

Solution:

x>4x > 4

Would you like more details on solving inequalities or any other questions?


Here are five related questions to explore:

  1. What is the solution set of 5x73x+95x - 7 \leq 3x + 9?
  2. How do you solve the inequality 2(x3)62(x - 3) \geq 6?
  3. How does solving inequalities differ from solving equalities?
  4. What happens when you multiply or divide by a negative number in an inequality?
  5. Can you graph the solution to x>4x > 4 on a number line?

Tip: When multiplying or dividing both sides of an inequality by a negative number, remember to reverse the inequality sign.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Basic linear inequality manipulation: Add or subtract terms and divide or multiply to isolate the variable

Theorems

Properties of inequalities, including flipping the inequality sign when multiplying or dividing by a negative number

Suitable Grade Level

Grades 6-8