(c) \( 2:(x+7)-x-20)=9 \)

To solve the equation \( 2:(x+7)-x-20=9 \), let's break it down step-by-step. The first thing is to clarify the use of the colon; if it indicates division, we can rewrite it as \( \frac{2}{x+7} - x - 20 = 9 \). Rearranging gives us \( \frac{2}{x+7} = x + 29 \). Multiplying both sides by \( x+7 \) helps eliminate the fraction, yielding \( 2 = (x + 29)(x + 7) \). From here, expand and arrange into a standard quadratic form to find the solution for \( x \). Now, it's crucial to check your work! A common mistake is losing track of signs when rearranging terms or expanding polynomials. Always double-check your steps and plug your solutions back into the original equation to verify they satisfy it. Happy solving!