To solve the equation \( x - 1 = -5 - x \), let's follow these steps:

1. Add \( x \) to both sides of the equation to eliminate the \( -x \) on the right-hand side:
   \[
   x - 1 + x = -5 - x + x
   \]
   This simplifies to:
   \[
   2x - 1 = -5
   \]

2. Add 1 to both sides to isolate the term with \( x \):
   \[
   2x - 1 + 1 = -5 + 1
   \]
   Simplifying this:
   \[
   2x = -4
   \]

3. Divide both sides by 2 to solve for \( x \):
   \[
   x = \frac{-4}{2}
   \]
   \[
   x = -2
   \]

So, the solution is \( x = -2 \).

Would you like further explanation or have any questions? Here are five related problems you might want to try:

1. \( 2x - 3 = 7 - x \)
2. \( x + 5 = 3 - 2x \)
3. \( 3x + 1 = 2x - 4 \)
4. \( 4x - 2 = 6x + 3 \)
5. \( -x + 6 = 10 + 2x \)

**Tip:** When solving linear equations, always aim to isolate the variable on one side.

Discover how to solve the linear equation x - 1 = -5 - x with a detailed, step-by-step explanation. This solution covers essential algebraic concepts such as isolating the variable, using equality properties, and dividing by coefficients. Ideal for students in Grades 6-8.

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