2 x + 16 = a x + 8 In the given equation, a is a constant. If the equation

Question

2 x + 16 = a x + 8 In the given equation, a is a constant. If the equation has infinitely many solutions, what is the value of a ?

Accepted Answer

The correct answer is 2 . An equation with one variable, x , has infinitely many solutions only when both sides of the equation are equal for any defined value of x . It's given that 2 x + 16 = a x + 8 , where a is a constant. This equation can be rewritten as 2 x + 8 = a x + 8 . If this equation has infinitely many solutions, then both sides of this equation are equal for any defined value of x . Both sides of this equation are equal for any defined value of x when 2 = a . Therefore, if the equation has infinitely many solutions, the value of a is 2 . Alternate approach: If the given equation, 2 x + 16 = a x + 8 , has infinitely many solutions, then both sides of this equation are equal for any value of x . If x = 0 , then substituting 0 for x in 2 x + 16 = a x + 8 yields 2 0 + 16 = a 0 + 8 , or 16 = 8 a . Dividing both sides of this equation by 8 yields 2 = a .

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