Let's solve the equation zero equals x plus two x. We need to find the value of x that makes this equation true. The key is to combine like terms on the right side.
Step one is to combine like terms. The terms x and two x are like terms because they both contain the variable x. We can combine them by adding their coefficients: one plus two equals three. So x plus two x becomes three x, and our equation becomes zero equals three x.
Step two is to divide both sides by three to isolate x. When we divide zero by three, we get zero. When we divide three x by three, the threes cancel out and we get x. Therefore, our final answer is zero equals x, or x equals zero.
Let's verify our answer by substituting x equals zero back into the original equation. Zero equals zero plus two times zero, which simplifies to zero equals zero plus zero, or zero equals zero. This is true, so our solution is correct. The answer is x equals zero.
To summarize what we learned: We solved the linear equation zero equals x plus two x by combining like terms to get three x, then dividing both sides by three to find that x equals zero. We verified this solution by substituting back into the original equation.