How do I solve 3/8x - 4 = 1/8x - 5

Question

I need to understand how to solve for fractions

Answer 1

... or perhaps:  3/(8x - 4) = 1/(8x - 5).

 

Multiply each side by (8x - 4)(8x - 5) to get 3(8x - 5) = 1(8x - 4).

 

This becomes:  24x - 15 = 8x - 4

 

simplifying:  16x = 11

 

                    x = 11/16

Answer 2

I'm not sure if the problem is (3/8)x - 4 = (1/8)x - 5 or 3/8x - 4 = 1/8x - 5.  I'll solve both.

 

(3/8)x - 4 = (1/8)x - 5

 

Subtract (1/8)x from both sides and add 4 to both sides:

 

(2/8)x = -1

(1/4)x = -1

 

Multiply both sides by 4:

 

x = -4

 

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3/8x - 4 = 1/8x - 5

 

Subtract  1/8x from both sides and add 4 to both sides:

 

3/8x - 1/8x = -1

2/8x = -1

1/4x = -1

 

Multiply both sides by -x:

 

1/(-4) = x

 

-1/4 = x