5 ( x + 7 ) = 15 x - 17 x + 7 What is the sum of the

Question

5 ( x + 7 ) = 15 x - 17 x + 7 What is the sum of the solutions to the given equation?

Accepted Answer

The correct answer is 31 3 . Subtracting 5 x + 7 from each side of the given equation yields 0 = 15 x - 17 x + 7 - 5 x + 7 . Since 5 x + 7 is a common factor of each of the terms on the right-hand side of this equation, it can be rewritten as 0 = 5 x + 7 3 x - 17 - 1 . This is equivalent to 0 = 5 x + 7 3 x - 51 - 1 , or 0 = 5 x + 7 3 x - 52 . Dividing both sides of this equation by 5 yields 0 = x + 7 3 x - 52 . Since a product of two factors is equal to 0 if and only if at least one of the factors is 0 , either x + 7 = 0 or 3 x - 52 = 0 . Subtracting 7 from both sides of the equation x + 7 = 0 yields x = - 7 . Adding 52 to both sides of the equation 3 x - 52 = 0 yields 3 x = 52 . Dividing both sides of this equation by 3 yields x = 52 3 . Therefore, the solutions to the given equation are - 7 and 52 3 . It follows that the sum of the solutions to the given equation is - 7 + 52 3 , which is equivalent to - 21 3 + 52 3 , or 31 3 . Note that 31/3 and 10.33 are examples of ways to enter a correct answer.

Question 5-x-7-