Final answer:
The English statement 'The difference between w and 32 equals five times w' translates to the mathematical equation w - 32 = 5w, which upon simplification gives the solution w = -8.
Step-by-step explanation:
The English statement 'The difference between w and 32 equals five times w' can be translated into a mathematical equation as follows: w - 32 = 5w. To solve the equation for w, we will add or subtract the same number from both sides of the equation as per LibreTexts™ guidelines. This will not change the equality. Hence, subtracting w from both sides, we get -32 = 4w. Now dividing both sides by 4 to solve for w, we have w = -8.