Question

John and Tammy cannot agree about the following statement: "If x = 9 and 4x - 7 = y, then 4(9) - 7 = y." John says this is the substitution property of equality and Tammy says it's the distributive property. Who is correct? Explain your reasoning.

Answer 1

John is correct. The substitution property is being used. The x is being substituted for the value 9 (aka x is replaced with 9). Keep in mind that x is simply a placeholder for a number, in this case 9. 

Think of "substitution" as in a sports game where one player replaces another. Or you can think of a substitute teacher where someone else temporarily replaces your teacher for the day. Those are two ways to help remember the term.

The distributive property is not being used here since it is a*(b+c) = a*b+a*c. For example, 2*(3+5) = 2*3+2*5