Final answer:
The reason for the given statement in solving the equation -191 + 4x = 145 - 10x is Combining Like Terms and Properties of Equality, where 10x is added to both sides of the equation in order to isolate the variable x.
Step-by-step explanation:
The student is asking to fill in the statement or reason for a step in solving the linear equation -191 + 4x = 145 - 10x. The given statement is -191 + 14x = 145, implying that the equations have been combined by adding 10x to each side.
The correct reason for this step is Combining Like Terms and the Properties of Equality. These properties allow you to add or subtract the same value from both sides of an equation to maintain equality. Specifically, 10x was added to both sides to get all the x terms on one side and simplify the equation. The statement itself is the result of this operation.
The step-by-step explanation is as follows: You start with the original equation, -191 + 4x = 145 - 10x, and then add 10x to both sides of the equation to get -191 + 14x = 145, which is the statement provided. This step is part of the process to isolate the variable x on one side of the equation, setting the stage for eventually solving for x.