- 5 x + 13 = 73 What is the sum of the solutions to the given equation?

Question

Accepted Answer

Choice D is correct. By the definition of absolute value, if $- 5 x + 13| = 73$ , then $- 5 x + 13 = 73$ or $- 5 x + 13 = - 73$ . Subtracting $13$ from both sides of the equation $- 5 x + 13 = 73$ yields $- 5 x = 60$ . Dividing both sides of this equation by $negative 5$ yields $x = - 12$ . Subtracting $13$ from both sides of the equation $- 5 x + 13 = - 73$ yields $- 5 x = - 86$ . Dividing both sides of this equation by $negative 5$ yields $x = \frac{86}{5}$ . Therefore, the solutions to the given equation are $negative 12$ and $StartFraction 86 Over 5 EndFraction$ , and it follows that the sum of the solutions to the given equation is $- 12 + \frac{86}{5}$ , or $StartFraction 26 Over 5 EndFraction$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is a solution, not the sum of the solutions, to the given equation.

Choice C is incorrect and may result from conceptual or calculation errors.

Question 5-x-13

- 5 x + 13 = 73 What is the sum of the solutions to the

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