Solved examples: applying properties of equality in equations (Grade 7)

📚 Quick Study Guide

• ⚖️ The Addition Property of Equality: If $a = b$, then $a + c = b + c$. Adding the same value to both sides maintains equality.
• ➖ The Subtraction Property of Equality: If $a = b$, then $a - c = b - c$. Subtracting the same value from both sides maintains equality.
• ✖️ The Multiplication Property of Equality: If $a = b$, then $a \cdot c = b \cdot c$. Multiplying both sides by the same value maintains equality.
• ➗ The Division Property of Equality: If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. Dividing both sides by the same non-zero value maintains equality.
• 🔄 The Substitution Property of Equality: If $a = b$, then $a$ can be substituted for $b$ in any equation.
• 🌱 The Distributive Property: $a(b + c) = ab + ac$. Useful for simplifying expressions before applying other properties.

✍️ Practice Quiz

1. What property of equality is used to solve the equation $x + 5 = 12$ by subtracting 5 from both sides?
   1. Addition Property
   2. Subtraction Property
   3. Multiplication Property
   4. Division Property
2. Solve for $x$: $3x = 21$
   1. $x = 3$
   2. $x = 7$
   3. $x = 24$
   4. $x = 63$
3. What is the first step in solving the equation $2x - 4 = 8$?
   1. Divide both sides by 2
   2. Subtract 4 from both sides
   3. Add 4 to both sides
   4. Multiply both sides by 2
4. Solve for $y$: $y - 7 = 3$
   1. $y = -4$
   2. $y = 4$
   3. $y = 10$
   4. $y = 21$
5. Which property justifies the step from $5(x + 2) = 15$ to $5x + 10 = 15$?
   1. Addition Property
   2. Distributive Property
   3. Multiplication Property
   4. Substitution Property
6. Solve for $z$: $\frac{z}{4} = 6$
   1. $z = \frac{3}{2}$
   2. $z = 2$
   3. $z = 10$
   4. $z = 24$
7. What property is used when you replace 'a' with '3' in the expression $a + 5$ if $a = 3$?
   1. Addition Property
   2. Subtraction Property
   3. Substitution Property
   4. Division Property