Question: 1) More than 2 times a # F- 2) 7 less than 5 times a # H- 3) 5 times a #, decreased by 2 E- 4) 2 diminished by 7 times a # I- 5) 2 increased by 5 times a # S- 6) Twice a #, decreased by 7 T- 7) 2 more than 7 times a # G- 8) 9 less than a # A- 9) 4 times a #, plus 9 I- 10) 9 diminished by 4 times a # T- 11) One-fourth of a # O- 12) 9 times a # decreased by 4 S- 13) 4 more than 9 times a # E- 14) 9 times a #, increased by 4 times the #

1. The problem asks to express "More than 2 times a #" algebraically. 2. The phrase "More than 2 times a #" means we start with $2 \times \# = 2x$ and then add something more. Since "more than" implies addition, the expression is $2x + \text{(some positive amount)}$. However, since no specific amount is given, the simplest interpretation is just $2x$ plus an unspecified positive amount. 3. For clarity, we interpret "More than 2 times a #" as $2x + k$ where $k > 0$ is unspecified. 4. Similarly, for each phrase: - "7 less than 5 times a #" means $5x - 7$. - "5 times a #, decreased by 2" means $5x - 2$. - "2 diminished by 7 times a #" means $2 - 7x$. - "2 increased by 5 times a #" means $2 + 5x$. - "Twice a #, decreased by 7" means $2x - 7$. - "2 more than 7 times a #" means $7x + 2$. - "9 less than a #" means $x - 9$. - "4 times a #, plus 9" means $4x + 9$. - "9 diminished by 4 times a #" means $9 - 4x$. - "One-fourth of a #" means $\frac{x}{4}$. - "9 times a # decreased by 4" means $9x - 4$. - "4 more than 9 times a #" means $9x + 4$. - "9 times a #, increased by 4 times the #" means $9x + 4x = 13x$. 5. These expressions translate the verbal phrases into algebraic expressions using $x$ to represent the # symbol. Final answers: 1) $2x + k$ (where $k > 0$ unspecified) 2) $5x - 7$ 3) $5x - 2$ 4) $2 - 7x$ 5) $2 + 5x$ 6) $2x - 7$ 7) $7x + 2$ 8) $x - 9$ 9) $4x + 9$ 10) $9 - 4x$ 11) $\frac{x}{4}$ 12) $9x - 4$ 13) $9x + 4$ 14) $13x$