How do you solve the equation 2x + 5 = 2 for x, and how can you determine if the solution is extraneous?

by

Solving the Equation

To solve the equation 2x + 5 = 2, we will start by isolating x. Here are the steps:

  1. Subtract 5 from both sides of the equation:

    2. 2x + 5 - 5 = 2 - 5

    This simplifies to:

    2x = -3

  2. Next, divide both sides by 2:

    3. x = -3 / 2

    So, we find

    x = -1.5

Checking for Extraneous Solutions

An extraneous solution is one that emerges from the process of solving an equation but does not satisfy the original equation. In this case, we need to check if x = -1.5 is indeed a solution of the original equation.

Let’s substitute -1.5 back into the original equation:

2(-1.5) + 5 = 2

This simplifies as follows:

  • -3 + 5 = 2
  • 2 = 2

Since the left-hand side equals the right-hand side, our solution x = -1.5 is valid, meaning it is not an extraneous solution.

Conclusion

Thus, the solution for the equation 2x + 5 = 2 is x = -1.5, and it is confirmed to be a true solution without being extraneous.

Leave a Comment