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

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