Solve the equation , and verify your answer.

 

You know from question that , so the solutions x = 1 and x = -4 fit this restrictions.

 

However, you also have to verify your solution. This means checking to see if the answer is correct. If the answer is correct when you substitute it into the original equation, the left side of the equation will equal the right side.

Verify the solution x = 1.

When the solution x = 1 is substituted into the original equation, the left side of the equation equals the right side of the equation. This means the solution x = 1 is verified to be correct.

Follow the same steps to verify x = -4

When the solution x = -4 is substituted into the original equation, the result is integers in both the numerator and denominator. Because factorials are not defined for integers, this means the solution x = -4 is not valid.

Therefore, the only valid solution is x = 1 because the equation is undefined when x = -4.

 

Read page 80 Example 4 in your textbook, Principles of Mathematics 12 .

Complete the Your Turn question on page 80 for more practice solving equations involving factorial notation.

Click here to verify your answer .