1. The problem asks to select all equations NOT equivalent to $p - 7 = 22$. 2. Start with the original equation: $$p - 7 = 22$$ 3. Check each option by simplifying and comparing to the original: - Option 1: $p - p - 7 = 22 - p$ Simplify left side: $\cancel{p} - \cancel{p} - 7 = -7$ Right side: $22 - p$ So equation is $-7 = 22 - p$, which is NOT equivalent to original. - Option 2: $p - 7 - p = 22 - p$ Simplify left side: $\cancel{p} - 7 - \cancel{p} = -7$ Right side: $22 - p$ Equation: $-7 = 22 - p$, NOT equivalent. - Option 3: $p - 7 + 22 = 22 - 7$ Simplify left side: $p + (22 - 7) = p + 15$ Right side: $15$ Equation: $p + 15 = 15$ Subtract 15 both sides: $$p + 15 - 15 = 15 - 15$$ $$p = 0$$ Original solution is $p = 29$, so NOT equivalent. - Option 4: $p - 7 + 7 = 22 - 22$ Simplify left side: $p - \cancel{7} + \cancel{7} = p$ Right side: $0$ Equation: $p = 0$ Not equivalent to original. - Option 5: $p - 7 + 7 = 22 + 7$ Simplify left side: $p - \cancel{7} + \cancel{7} = p$ Right side: $29$ Equation: $p = 29$ This matches the original solution, so equivalent. 4. Therefore, the equations NOT equivalent to $p - 7 = 22$ are options 1, 2, 3, and 4.