Question

1. make up your own equation, and show an example of using the addition property of equality. you do not have to solve the equation.

1. make up your own equation, and show an example of using the subtraction property of equality. you do not have to solve the equation.

1. make up your own equation, and show an example of using the division property of equality. you do not have to solve the equation.

1. make up your own equation, and show an example of using the multiplication property of equality. you do not have to solve the equation.

1. make up your own equation, and show an example of using the distributive property. you do not have to solve the equation.

Explanation:

Step1: Define original equation

$x - 7 = 12$

Step2: Apply addition property

Add 9 to both sides: $x - 7 + 9 = 12 + 9$

Step1: Define original equation

$y + 4 = 19$

Step2: Apply subtraction property

Subtract 6 from both sides: $y + 4 - 6 = 19 - 6$

Step1: Define original equation

$3z = 21$

Step2: Apply division property

Divide both sides by 3: $\frac{3z}{3} = \frac{21}{3}$

Step1: Define original equation

$\frac{w}{5} = 8$

Step2: Apply multiplication property

Multiply both sides by 4: $4 \times \frac{w}{5} = 8 \times 4$

Step1: Define original equation

$5(2a + 3) = 40$

Step2: Apply distributive property

Expand left side: $5 \times 2a + 5 \times 3 = 40$

Answer:

1. Original equation: $x - 7 = 12$; Using addition property: $x - 7 + 9 = 12 + 9$
2. Original equation: $y + 4 = 19$; Using subtraction property: $y + 4 - 6 = 19 - 6$
3. Original equation: $3z = 21$; Using division property: $\frac{3z}{3} = \frac{21}{3}$
4. Original equation: $\frac{w}{5} = 8$; Using multiplication property: $4 \times \frac{w}{5} = 8 \times 4$
5. Original equation: $5(2a + 3) = 40$; Using distributive property: $10a + 15 = 40$