To solve the equation \( 4x + 32 = 12x - 24 \), we follow these steps:

### Step 1: Move the terms involving \(x\) to one side
Subtract \(4x\) from both sides:
\[
32 = 12x - 4x - 24
\]
Simplify:
\[
32 = 8x - 24
\]

### Step 2: Move the constants to the other side
Add 24 to both sides:
\[
32 + 24 = 8x
\]
Simplify:
\[
56 = 8x
\]

### Step 3: Solve for \(x\)
Divide both sides by 8:
\[
x = \frac{56}{8}
\]
\[
x = 7
\]

The solution is \( x = 7 \).

Would you like more details on the steps? Here are five related questions you might find useful:

1. How do you solve equations with variables on both sides?
2. What if the equation had decimals or fractions? 
3. How can you check if the solution is correct?
4. What happens if both sides of the equation have no solution?
5. How can this problem be applied in real-life situations?

**Tip**: Always simplify both sides of the equation as much as possible before isolating the variable.

Learn how to solve the linear equation 4x + 32 = 12x - 24 with step-by-step guidance. This solution covers core algebraic concepts such as isolating variables and applying the properties of equality. Ideal 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