Let's solve the equation \( 5x - 2 = 3x + 4 \):

### Step-by-Step Solution:
1. Start by subtracting \( 3x \) from both sides to get all the terms with \( x \) on one side:
   \[
   5x - 3x - 2 = 4
   \]
   Simplifying:
   \[
   2x - 2 = 4
   \]

2. Next, add \( 2 \) to both sides to isolate the term with \( x \):
   \[
   2x = 6
   \]

3. Finally, divide both sides by \( 2 \) to solve for \( x \):
   \[
   x = \frac{6}{2} = 3
   \]

### Solution:
The solution is \( x = 3 \).

Would you like further details or have any other questions?

Here are five related questions to expand on this:
1. What happens if you change the equation to \( 5x - 2 = 3x + 6 \)?
2. How would you solve \( 5x - 2 = 4x + 4 \)?
3. What are the steps to solve \( 2(5x - 2) = 3(3x + 1) \)?
4. How would you handle an equation with a fraction like \( \frac{5x - 2}{3} = \frac{3x + 4}{2} \)?
5. How do you solve an inequality like \( 5x - 2 > 3x + 4 \)?

### Tip:
Always remember to isolate the variable step by step, using inverse operations like addition, subtraction, multiplication, and division.

Learn how to solve the linear equation 5x - 2 = 3x + 4 with a step-by-step guide. This problem focuses on key algebraic concepts such as isolating variables and applying the properties of equality. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation