Final answer:
The equation 18-2x=4x is solved by adding 2x to both sides to consolidate the x terms, resulting in 18=6x, and then by dividing both sides by 6 to solve for x, obtaining x=3.
Step-by-step explanation:
The reason for each step in the solution of the equation 18-2x=4x stems from the need to isolate the variable x to find its value. To solve for x, we must get all the x's on one side of the equation and the constants on the other. This is achieved through a series of algebraic manipulations.
First, we want to combine like terms, specifically the terms containing x. To accomplish this, we add 2x to both sides of the equation to move the negative term on the left side to the right, resulting in 18=6x. Now that we have consolidated the x terms, we divide both sides of the equation by 6 to solve for x, leading us to x = 3. The purpose of these steps is to use algebraic principles to simplify the equation to a point where x is clearly defined.