Question

Factor 1/4 out of -1/2x - 5/4y

Answer 1

One solution was found :                   y = 1/13 = 0.077

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                1/7*y-1/4-(-5/4*y-1/7)=0 

Step by step solution :Skip Ad
Step  1  : 1 Simplify — 7 Equation at the end of step  1  : 1 1 5 1 ((—•y)-—)-((0-(—•y))-—) = 0 7 4 4 7 Step  2  : 5 Simplify — 4 Equation at the end of step  2  : 1 1 5 1 ((—•y)-—)-((0-(—•y))-—) = 0 7 4 4 7 Step  3  :Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple 

      The left denominator is :       4 

      The right denominator is :       7 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 22027011 Product of all 
 Prime Factors 4728

      Least Common Multiple: 
      28 

Calculating Multipliers :

 3.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 7

   Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

 3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well. 

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respectiveMultiplier.

L. Mult. • L. Num. -5y • 7 —————————————————— = ——————— L.C.M 28 R. Mult. • R. Num. 4 —————————————————— = —— L.C.M 28 Adding fractions that have a common denominator :

 3.4       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-5y • 7 - (4) -35y - 4 ————————————— = ———————— 28 28 Equation at the end of step  3  : 1 1 (-35y - 4) ((— • y) - —) - —————————— = 0 7 4 28 Step  4  : 1 Simplify — 4 Equation at the end of step  4  : 1 1 (-35y - 4) ((— • y) - —) - —————————— = 0 7 4 28 Step  5  : 1 Simplify — 7 Equation at the end of step  5  : 1 1 (-35y - 4) ((— • y) - —) - —————————— = 0 7 4 28 Step  6  :Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple 

      The left denominator is :       7 

      The right denominator is :       4 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 71012022 Product of all 
 Prime Factors 7428

      Least Common Multiple: 
      28 

Calculating Multipliers :

 6.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 4

   Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. y • 4 —————————————————— = ————— L.C.M 28 R. Mult. • R. Num. 7 —————————————————— = —— L.C.M 28 Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions 

y • 4 - (7) 4y - 7 ——————————— = —————— 28 28 Equation at the end of step  6  : (4y - 7) (-35y - 4) ———————— - —————————— = 0 28 28 Step  7  :Step  8  :Pulling out like terms :

 8.1     Pull out like factors :

   -35y - 4  =   -1 • (35y + 4) 

Adding fractions which have a common denominator :

 8.2       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(4y-7) - ((-35y-4)) 39y - 3 ——————————————————— = ——————— 28 28 Step  9  :Pulling out like terms :

 9.1     Pull out like factors :

   39y - 3  =   3 • (13y - 1) 

Equation at the end of step  9  : 3 • (13y - 1) ————————————— = 0 28 Step  10  :When a fraction equals zero : 10.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

3•(13y-1) ————————— • 28 = 0 • 28 28

Now, on the left hand side, the  28  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   3  •  (13y-1)  = 0

Equations which are never true :

 10.2      Solve :    3   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 10.3      Solve  :    13y-1 = 0 

 Add  1  to both sides of the equation : 
                      13y = 1 
Divide both sides of the equation by 13:
                     y = 1/13 = 0.077 

One solution was found :                   y = 1/13 = 0.077