Solving the Absolute Value Equation: Discover x When |x - 1| = 6

To solve the equation $|x-1| = 6$, we will use the definition of absolute value to create two separate linear equations:

• Equation 1: $x - 1 = 6$
• Equation 2: $x - 1 = -6$

Let's solve each equation separately:

For the first equation $x - 1 = 6$:

• Add 1 to both sides of the equation:
  $x - 1 + 1 = 6 + 1$
  This simplifies to $x = 7$.

For the second equation $x - 1 = -6$:

• Add 1 to both sides of the equation:
  $x - 1 + 1 = -6 + 1$
  This simplifies to $x = -5$.

Thus, the solutions to the equation $|x-1| = 6$ are $x = -5$ and $x = 7$.

Therefore, the correct solutions are $x = -5$ and $x = 7$.