I need help solving rational equations, i cant figure out how

Question

The problem is

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

Answer 1

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

 

It looks like there is a confusion about the parenthesis.  

 

Start by distributing the negative sign ("remove" the negative)

 

2x + 1/3 - x + 5/4 = 1/2

 

Combine like terms, the x's.

 

x + 1/3 + 5/4 = 1/2

 

Get rid of the fractions.  It easier for me to think in whole numbers so I multiply everything by the numbers in the denominators (2, 3 and 4).  In this case just 3 and 4 are enough since 2 is a factor of 4.

 

Multiply all terms by 12.  12 is 3 x 4

 

12x + 4 + 15 = 6

 

Combine the whole numbers

 

12x + 19 = 6

 

Subtract 19 from both sides.

 

12x = -13

 

Divide both sides by 12

 

x = -13/12

 

Change the answer to a mixed number

 

x = -1 1/12

Answer 2

Daisy, you have to use parentheses to avoid double reading!!!!
(2x + 1)/3 – (x + 5)/4 = 1/2

LCD(2, 3, 4) = 12

.   (2x + 1) • 6         (x + 5) • 3       1 • 4  
.  ———————  –  ——————  =  ——— 
.       2 • 6                  4 • 3            3 • 4 

.  12x + 6 – 3x –  15             4
.  —————————— = ——
.            12                         12

9x – 9 = 4
9x = 4 + 9
9x = 13
.          13               4 
 x  =  ———  =  1 ——
.           9               9