3 - (x + 5) = -3x. do the same for this problem 

Let's solve the equation \(3 - (x + 5) = -3x\) and then check the solution.

### Step 1: Solve the Equation

1. Start with the equation:
   \[
   3 - (x + 5) = -3x
   \]

2. Distribute the negative sign through the parentheses:
   \[
   3 - x - 5 = -3x
   \]

3. Simplify the left side by combining like terms:
   \[
   -x - 2 = -3x
   \]

4. Add \(3x\) to both sides to move the variable terms to one side:
   \[
   3x - x - 2 = 0
   \]

5. Combine like terms:
   \[
   2x - 2 = 0
   \]

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

7. Divide both sides by 2 to solve for \(x\):
   \[
   x = \frac{2}{2} = 1
   \]

So, the solution is \(x = 1\).

### Step 2: Check the Solution

To verify the solution, substitute \(x = 1\) back into the original equation:

1. Start with the original equation:
   \[
   3 - (x + 5) = -3x
   \]

2. Substitute \(x = 1\):
   \[
   3 - (1 + 5) = -3(1)
   \]

3. Simplify both sides:
   \[
   3 - 6 = -3
   \]

4. Simplify further:
   \[
   -3 = -3
   \]

Since both sides of the equation are equal, the solution \(x = 1\) is correct.

Would you like further details or have any questions?

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Here are 8 related questions for further exploration:

1. How would you solve \(4 - (2x + 3) = -2x\)?
2. What happens if the equation is \(3 - (x + 5) = -4x\)?
3. How do you solve \(7 - (x + 2) = -5x\)?
4. What is the solution to \(2 - (x + 1) = -x - 3\)?
5. How do you handle an equation like \(5 - (2x - 3) = 4x\)?
6. What happens if the equation is \(3 - (x + 5) = -2x - 3\)?
7. How would you check the solution to \(2 - (x + 4) = -x\)?
8. What is the effect of changing the constant term in \(3 - (x + 5) = -3x\)?

**Tip:** When solving equations with parentheses, remember to distribute any negative signs carefully to avoid mistakes.

Learn how to solve the equation 3 - (x + 5) = -3x with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, the distributive property, and combining like terms. Suitable for students in Grades 7-9.

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