0.2(x-1)-3.2x=0.5(6x+3)-1.2
Can someone tell me all the steps thxs

Step-by-step explanation:

One solution :

                  x = -1/12 = -0.083

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.2" was replaced by "(12/10)". 4 more similar replacement(s)

Rearrange:

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

     (2/10)*(x-1)-(32/10)*x-((5/10)*(6*x+3)-(12/10))=0

Step by step solution :

Step  1  :

           6

Simplify   —

           5

Equation at the end of step  1  :

    2         32        5         6

 ((——•(x-1))-(——•x))-((——•(6x+3))-—)  = 0

   10         10       10         5

Step  2  :

           1

Simplify   —

           2

Equation at the end of step  2  :

    2         32       1         6

 ((——•(x-1))-(——•x))-((—•(6x+3))-—)  = 0

   10         10       2         5

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  6x + 3  =   3 • (2x + 1)

Equation at the end of step  4  :

    2         32      3•(2x+1) 6

 ((——•(x-1))-(——•x))-(————————-—)  = 0

   10         10         2     5

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple

     The left denominator is :       2

     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}

2101

5011

Product of all

Prime Factors  2510

     Least Common Multiple:

     10

Calculating Multipliers :

5.2    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 :

5.3      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 respective Multiplier.

  L. Mult. • L. Num.      3 • (2x+1) • 5

  ——————————————————  =   ——————————————

        L.C.M                   10      

  R. Mult. • R. Num.      6 • 2

  ——————————————————  =   —————

        L.C.M              10  

Adding fractions that have a common denominator :

5.4       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:

3 • (2x+1) • 5 - (6 • 2)     30x + 3

————————————————————————  =  ———————

           10                  10  

Equation at the end of step  5  :

    2         32     (30x+3)

 ((——•(x-1))-(——•x))-———————  = 0

   10         10       10  

Step  6  :

           16

Simplify   ——

           5

Equation at the end of step  6  :

    2         16     (30x+3)

 ((——•(x-1))-(——•x))-———————  = 0

   10         5        10  

Step  7  :

           1

Simplify   —

           5

Equation at the end of step  7  :

   1               16x     (30x + 3)

 ((— • (x - 1)) -  ———) -  —————————  = 0

   5                5         10    

Step  8  :

Equation at the end of step  8  :

  (x - 1)    16x     (30x + 3)

 (——————— -  ———) -  —————————  = 0

     5        5         10    

Step  9  :

Adding fractions which have a common denominator :

9.1       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:

(x-1) - (16x)     -15x - 1

—————————————  =  ————————

      5              5    

Equation at the end of step  9  :

 (-15x - 1)    (30x + 3)

 —————————— -  —————————  = 0

     5            10    

Step  10  :

Step  11  :

Pulling out like terms :

11.1     Pull out like factors :

  -15x - 1  =   -1 • (15x + 1)

Step  12  :

Pulling out like terms :

12.1     Pull out like factors :

  30x + 3  =   3 • (10x + 1)