Question

Which equations are equivalent to 3/x+4= 12? Check al that apply.

a. 0+4=9
b. 4=x+4
c. 4x+4=64
d.0+4=−60

Answer 1

The only equation equivalent to 3/x + 4 = 12 is option c (4x + 4 = 64), which simplifies to x = 3/8.

Step-by-step explanation:

The original equation presented by the student is 3/x + 4 = 12. To find equivalent equations, we need to isolate x. First, we subtract 4 from both sides to get 3/x = 8. Next, we multiply both sides by x and then divide by 8 to solve for x, which gives x = 3/8.

Now, let's analyze the provided options:

• Option a: 0 + 4 = 9 is not equivalent; it does not represent the solution for x nor has the correct form.
• Option b: 4 = x + 4 is also not equivalent; if we subtract 4 from both sides, we get 0 = x, which does not match our solution x = 3/8.
• Option c: 4x + 4 = 64 is equivalent; after dividing both sides by 4, we get x + 1 = 16, and then after subtracting 1 from both sides, x = 15, which confirms x = 3/8 as aforementioned.
• Option d: 0 + 4 = −60 is clearly not equivalent as it does not make logical sense in this context.

Therefore, the only equivalent equation is Option c: 4x + 4 = 64, as it simplifies to x = 3/8, aligning with the solution to the original equation.