Answer:
1. Distributive property
2. Addition property of equality
3. Multiplication property of equality.
Step-by-step explanation:
We are given the following information in the question.
An equation is solved using various properties. We have to tell the properties used.
The solving of the equation is done in the following manner:
[tex]2(3x+5) = 22 + 5x - 3x\\\text{Using the distributive property: a(b+c) = ab + ac}\\6x + 10 = 22 + 5x - 3x\\6x + 10 = 22 + 2x\\\text{Using addition property of equality: If a = b then a+x = b + x}\\6x + 10 -2x = 22 + 2x -2x\\4x + 10 = 22\\\text{Using addition property of equality: If a = b then a+x = b + x}\\4x + 10 - 10 = 22-10\\4x = 12\\\text{Using multiplication property of equality: If a = b then ax = bx}\\\displaystyle\frac{4x}{34} = \frac{12}{4}\\\\x = 3[/tex]
Thus, the following properties were used:
1. Distributive property
2. Addition property of equality
3. Multiplication property of equality.
