Problem 70 - Introductory Algebra for College Students

Question

Explain why \(x+2=9\) and \(x+2=-6\) are not equivalent equations.

Step-by-Step Solution

Answer

The two equations \(x+2=9\) and \(x+2=-6\) are not equivalent because they have different solutions: \(x=7\) for the first equation and \(x=-8\) for the second one.

Step 1: Solve the First Equation

First, let's solve the equation \(x+2=9\). Start by isolating 'x' on one side. It means that we must subtract 2 from both sides of the equation. By doing so, you get \(x=9-2\) which simplifies to \(x=7\).

Step 2: Solve the Second Equation

Now, solve the second equation \(x+2=-6\). Similar to the first equation, isolate 'x' on one side by subtracting 2 from both sides of the equation. We get \(x=-6-2\) which simplifies to \(x=-8\).

Step 3: Compare the Two Solutions

Now that we have found the solutions to both equations, we can compare them. The solution for the first equation \(x+2=9\) is \(x=7\), and the solution for the second equation \(x+2=-6\) is \(x=-8\). Clearly, the solutions are not the same, therefore, the equations are not equivalent.