When you solve the equation x + 1 = 2x for x, the solution is 1. 1) Square both sides of the equation, and verify that your solution satisfies the new equation. 2) Show that −1/3 satisfies the new equation but not the original equation.

Part 1: The solution of the new equation is and and the two solutions satisfies the new equation.

Part 2: The solution satisfies the new equation but not the original equation.

Explanation:

Part 1: The given equation is

We need to square both sides of the equation and verify that the solution satisfies the new equation.

Now, squaring both sides of the equation, we get,

Thus, the new equation is

Let us solve the new equation to determine the solution.

Taking factors, we get,

Thus, the solution of the new equation is and

Now, we shall verify the solution and that satisfies the new equation

Substituting in , we get,

Since, both sides of the equation are equal, the solution satisfies the new equation.

Also, substituting in , we get,

Since, both sides of the equation are equal, the solution satisfies the new equation.

Thus, the solutions and satisfies the new equation.

Part 2: Now, we need to show that the solution satisfies the new equation but not the original equation.

Substituting in the new equation, we get,

Since, both sides of the equation are equal, the solution satisfies the new equation.

Now, substituting in the original equation, we have,

Since, both sides of the equation are not equal, the solution does not satisfies the original equation.

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