Solve the equation.  Write the solution set by using set notation.  Use braces { } for set notation. DO NOT enter use any spaces in your answer. 3 (2x + 4)=2(3x+6)

Let's solve the equation step by step:

Given:
\[
3(2x + 4) = 2(3x + 6)
\]

### Step 1: Distribute the constants.
On the left-hand side:
\[
3(2x + 4) = 6x + 12
\]
On the right-hand side:
\[
2(3x + 6) = 6x + 12
\]
So the equation becomes:
\[
6x + 12 = 6x + 12
\]

### Step 2: Subtract \(6x\) from both sides.
\[
6x + 12 - 6x = 6x + 12 - 6x
\]
This simplifies to:
\[
12 = 12
\]

### Step 3: Interpret the result.
The equation simplifies to \(12 = 12\), which is always true. This indicates that the equation holds for **all values of \(x\)**.

### Final Answer:
The solution set includes all real numbers. In set notation, this is written as:
\[
\boxed{\{x|x\in\mathbb{R}\}}
\]

Would you like further details or explanations on this?

Here are 5 related questions to explore:
1. What is the difference between an equation with all real solutions and one with no solutions?
2. How do you solve linear equations with variables on both sides?
3. What happens when you subtract the same variable term from both sides?
4. How can we check if an equation has infinitely many solutions?
5. What is the significance of distributing in equations?

**Tip:** Always check if the variables cancel out when simplifying equations, as this can lead to special solutions like "all real numbers" or "no solution."

Solve the equation. Write the solution set by using set notation. Use braces { } for set notation. DO NOT enter use any spaces in your answer. 3(2x + 4) = 2(3x + 6)

Learn how to solve the linear equation 3(2x + 4) = 2(3x + 6) step by step, applying the distributive property and interpreting the solution using set notation. This problem is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation