Question

Slove 3x/10+2x/5=7x/25+29/25

Answer 1

3x/10 + 2x/5 = 7x/25 + 29/25
(15x + 20x)/50 = (7x + 29)/25
35x/50 = (7x+29)/25
35x * 25 = 7x*50 + 29*50
875x = 350x + 1450
875x - 350x = 1450
525x = 1450
x = 1450/525 = 2.761

Answer 2

Step  1  :

29 Simplify —— 25

Equation at the end of step  1  :

x x x 29 ((3•——)+(2•—))-((7•——)+——) = 0 10 5 25 25

Step  2  :

x Simplify —— 25

Equation at the end of step  2  :

x x x 29 ((3•——)+(2•—))-((7•——)+——) = 0 10 5 25 25

Step  3  :

Adding fractions which have a common denominator :

 3.1       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:

7x + 29 7x + 29 ——————— = ——————— 25 25

Equation at the end of step  3  :

x x (7x+29) ((3•——)+(2•—))-——————— = 0 10 5 25

Step  4  :

x Simplify — 5

Equation at the end of step  4  :

x x (7x + 29) ((3 • ——) + (2 • —)) - ————————— = 0 10 5 25

Step  5  :

x Simplify —— 10

Equation at the end of step  5  :

x 2x (7x + 29) ((3 • ——) + ——) - ————————— = 0 10 5 25

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple 

      The left denominator is :       10 

      The right denominator is :       5 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 21015111 Product of all 
 Prime Factors 10510


      Least Common Multiple: 
      10 

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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. 3x —————————————————— = —— L.C.M 10 R. Mult. • R. Num. 2x • 2 —————————————————— = —————— L.C.M 10

Adding fractions that have a common denominator :

 6.4       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:

3x + 2x • 2 7x ——————————— = —— 10 10

Equation at the end of step  6  :

7x (7x + 29) —— - ————————— = 0 10 25

Step  7  :

Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple 

      The left denominator is :       10 

      The right denominator is :       25 

        Number of times each prime factor
        appears in the factorization of: Prime 
 Factor  Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 {Left,Right} 21015122 Product of all 
 Prime Factors 102550


      Least Common Multiple: 
      50 

Calculating Multipliers :

 7.2    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 = 5

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. 7x • 5 —————————————————— = —————— L.C.M 50 R. Mult. • R. Num. (7x+29) • 2 —————————————————— = ——————————— L.C.M 50

Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions 

7x • 5 - ((7x+29) • 2) 21x - 58 —————————————————————— = ———————— 50 50

Equation at the end of step  7  :

21x - 58 ———————— = 0 50

Step  8  :

When a fraction equals zero :

 8.1    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:

21x-58 —————— • 50 = 0 • 50 50

Now, on the left hand side, the  50  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   21x-58  = 0

Solving a Single Variable Equation :

 8.2      Solve  :    21x-58 = 0 

 Add  58  to both sides of the equation : 
                      21x = 58 
Divide both sides of the equation by 21:
                     x = 58/21 = 2.762 

One solution was found :

                   x = 58/21 = 2.762


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