Question

Solve |5x + 60| = 10x. Identify the solution and an extraneous solution.

a. x = 5, extraneous solution: x = -5
b. x = 5, extraneous solution: x = 6
c. x = 6, extraneous solution: x = -5
d. x = 6, extraneous solution: x = 5

Answer 1

To solve the equation |5x + 60| = 10x, we consider two cases: when 5x + 60 is positive and when it is negative. The solution is x = 12 and the extraneous solution is x = -4.

Step-by-step explanation:

To solve the equation |5x + 60| = 10x, we need to consider two cases: when 5x + 60 is positive and when it is negative.

Case 1: 5x + 60 is positive. In this case, the equation becomes 5x + 60 = 10x. Subtracting 5x from both sides, we get 60 = 5x. Dividing both sides by 5, we find x = 12.

Case 2: 5x + 60 is negative. In this case, the equation becomes -(5x + 60) = 10x. Distributing the negative sign, we get -5x - 60 = 10x. Adding 5x to both sides, we get -60 = 15x. Dividing both sides by 15, we find x = -4.

So the solution is x = 12 and the extraneous solution is x = -4.