Let's solve the equation step by step:

Given equation:
\[
3(x + 2) - 2 = -(5 + x) + x
\]

### Step 1: Distribute and simplify both sides.
On the left-hand side, distribute the 3:
\[
3(x + 2) - 2 = 3x + 6 - 2
\]
Simplify:
\[
3x + 4
\]

On the right-hand side, distribute the negative sign:
\[
-(5 + x) + x = -5 - x + x
\]
Simplify:
\[
-5
\]

So the equation now is:
\[
3x + 4 = -5
\]

### Step 2: Isolate the variable \(x\).
Subtract 4 from both sides:
\[
3x = -5 - 4
\]
\[
3x = -9
\]

### Step 3: Solve for \(x\).
Divide both sides by 3:
\[
x = \frac{-9}{3}
\]
\[
x = -3
\]

### Final Answer:
\[
x = -3
\]

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What if the equation had been \(3(x + 2) - 2 = -2(5 + x) + x\)?
2. How would you solve \(4(x + 1) - 3 = 2x - 7\)?
3. What are the steps to solve \(5x + 7 = 2(x - 3)\)?
4. How can you check if your solution for \(x\) is correct?
5. How do you solve quadratic equations like \(x^2 + 5x + 6 = 0\)?
6. How does factoring compare to using the quadratic formula in solving quadratic equations?
7. What is the difference between solving an equation and simplifying an expression?
8. What if the equation had fractions, like \(\frac{3x}{2} + 4 = \frac{5}{x} - 1\)?

**Tip:** Always remember to check your solution by substituting it back into the original equation!

Learn how to solve the equation 3(x+2)-2=-(5+x)+x step-by-step with detailed explanations and examples. This problem covers solving linear equations and the application of distributive property. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation