1. The problem asks to identify the property of equality illustrated by each statement. 2. Recall some important properties of equality: - Reflexive Property: $a = a$ - Symmetric Property: If $a = b$, then $b = a$ - Transitive Property: If $a = b$ and $b = c$, then $a = c$ - Addition/Subtraction Property: If $a = b$, then $a + c = b + c$ - Multiplication/Division Property: If $a = b$, then $ac = bc$ and if $c \neq 0$, $\frac{a}{c} = \frac{b}{c}$ 3. Analyze each statement: 1) If $n + 1 = 4$ then $n = 3$. - This uses the Subtraction Property of Equality: subtract 1 from both sides. 2) $10 = 10$. - This is the Reflexive Property of Equality. 3) If $5 = x$, then $x = 5$. - This is the Symmetric Property of Equality. 4) If $x = 7$ and $y + 2 = x$, then $7 = y + 2$. - This is the Transitive Property of Equality. 5) If $2x = 12$, then $x = 6$. - This uses the Division Property of Equality: divide both sides by 2. 6) If $3x + 7 = 1$, then $3x = -6$. - This uses the Subtraction Property of Equality: subtract 7 from both sides. 7) If $16x = -8$, then $x = \frac{1}{2}$. - This is incorrect as $x = \frac{-8}{16} = -\frac{1}{2}$, so no property applies correctly here. 8) If $x = 2$, then $3x = 6$. - This uses the Multiplication Property of Equality: multiply both sides by 3. 9) If $x = 5$, then $5 + x = 2x$. - Substitute $x=5$ into both sides: $5 + 5 = 2 \times 5$, so $10 = 10$. - This is the Substitution Property of Equality. 10) If $3x + 12 = 21$, then $3x = 33$. - This is incorrect because subtracting 12 from 21 gives $3x = 9$, not 33. Final answers: 1) Subtraction Property of Equality 2) Reflexive Property of Equality 3) Symmetric Property of Equality 4) Transitive Property of Equality 5) Division Property of Equality 6) Subtraction Property of Equality 7) Incorrect statement (no property applies) 8) Multiplication Property of Equality 9) Substitution Property of Equality 10) Incorrect statement (no property applies)