when 12 is subtracted from a number the result is equal to 25 added to twice the number. Find the number.

1 answer

Let the number be represented by \( x \). According to the problem, when 12 is subtracted from the number, the result is equal to 25 added to twice the number. This can be set up in the form of an equation:

\[ x - 12 = 2x + 25 \]

Now, we can solve for \( x \). First, let's isolate \( x \) by moving all terms involving \( x \) to one side and constant terms to the other side:

  1. Subtract \( x \) from both sides:

\[ -12 = x + 25 \]

  1. Now, subtract 25 from both sides:

\[ -12 - 25 = x \] \[ -37 = x \]

Thus, the number is:

\[ \boxed{-37} \]

To verify, we can substitute \( x = -37 \) back into the original equation:

  • Subtracting 12 gives: \[ -37 - 12 = -49 \]

  • Calculating \( 2x + 25 \): \[ 2(-37) + 25 = -74 + 25 = -49 \]

Both sides are equal, confirming that the solution is correct. Therefore, the number is indeed \( \boxed{-37} \).