Question

What is the correct reason for statement 1 in the proof?

Multiplication Property of Equality
Given
Addition Property of Equality
Substitution Property

Answer 1

eflexive Property
For all real numbers x, x = x.

A number equals itself.

These three properties define an equivalence relation


Symmetric Property
For all real numbers x and y,

if x = y, then y = x.

Order of equality does not matter.

Transitive Property
For all real numbers x, y, and z ,

if x = y and y = z, then x = z.

Two numbers equal to the same number are equal to each other.

Addition Property
For all real numbers x, y, and z,

if x = y, then x + z = y + z.

These properties allow you to balance and solve equations involving real numbers
Subtraction Property
For all real numbers x, y, and z,

if x = y, then x – z = y – z.

Multiplication Property
For all real numbers x, y, and z,

if x = y, then xz = yz.

Division Property
For all real numbers x, y, and z,

if x = y, and z ≠ 0, then x/z = y/z.

Substitution Property
For all real numbers x and y ,

if x = y , then y can be substituted for x in any expression.

Distributive Property
For all real numbers x, y, and z,

x(y + z) = xy + xz.

For more, see the section on the distributive property