7. Winona and her mom buy ribbon to wrap presents. The cost of \( p \) inches of plain ribbon is represented by \( 6 p \). The cost of \( p \) inches of striped ribbon is represented by \( 6 p+9 \). Winona says that \( 6 p=6 p+9 \) for any value of \( p \) because the coefficients of \( p \) are the same on both sides of the equation. Is Winona correct? Explain.

Winona's assertion is incorrect because while the coefficients of \( p \) are the same on both sides, the constants differ. In her equation \( 6p = 6p + 9 \), subtracting \( 6p \) from both sides gives \( 0 = 9 \), which is obviously false. This indicates that these two expressions are not equal for any value of \( p \). The cost of the striped ribbon is consistently higher due to the additional $9, making it more expensive than the plain ribbon regardless of the length. To clarify, it's important to recognize that in an equation like \( 6p = 6p + c \), if \( c \) is not zero, the equation cannot be true. This common mistake often arises from overlooking constant values in algebraic expressions. Always ensure to evaluate both sides of an equation fully before concluding equality!