Question

Solve the equation. Show your work. (4 points)
(x + 5)/(8x) = 1/4 + 3/(2x)

Answer 1

That's not what I get:
(x + 5)/(8x) = 1/4 + 3/(2x)
(x+5) = 2x + 12
x = -7

Answer 2

To solve the equation, we need to find a common denominator for both sides.

Common denominator = 8x

Rewrite the equation with the common denominator:

(4*(x + 5))/(8x) = (2/(8x)) + (12/(8x))

Now simplify each side:

(4x + 20)/(8x) = (2 + 12)/(8x)

(4x + 20)/(8x) = 14/(8x)

Since the denominators are the same, we can set the numerators equal to each other:

4x + 20 = 14

Subtract 20 from both sides:

4x = -6

Divide by 4 on both sides:

x = -6/4

x = -3/2

Answer 3

You are correct. The correct steps to solve the equation are as follows:

(x + 5)/(8x) = 1/4 + 3/(2x)

Cross multiply to eliminate the fractions:

2(x + 5) = 8x + 24

Expand and simplify:

2x + 10 = 8x + 24

Subtract 2x from both sides:

10 = 6x + 24

Subtract 24 from both sides:

-14 = 6x

Divide by 6 on both sides:

x = -14/6

Simplify the fraction:

x = -7/3

Therefore, the correct solution to the equation is x = -7/3. Thank you for catching the mistake.