Final answer:
The justifications for solving the equation 4(x + 5) = 2x + 2 are distribution, subtraction property of equality, and division property of equality, following basic arithmetic and algebraic sign rules.
Step-by-step explanation:
The subject of the question is Mathematics, and the student appears to be in High School level based on the algebraic operations involved. The sequence of justifications required for each step in the student's problem are:
Distribution: The student used the distributive property to expand 4(x + 5) into 4x + 20.
Subtraction Property of Equality: Subtracting 2x from both sides gives 2x + 20 = 2.
Subtraction Property of Equality: Subtracting 20 from both sides gives 2x = -18.
Division Property of Equality: Dividing both sides by 2 gives x = -9.
It is also essential to remember that during subtraction and division, the sign rules must be followed, and that when solving algebraic equations like these, keeping balanced operations on both sides of the equality is crucial.