Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.1" was replaced by "(31/10)". 3 more similar replacement(s)

Rearrange:

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

           (18/10)-(2/10)*(3*w-5)-((31/10))≤0 

Step by step solution :

Step  1  :

            31
 Simplify   ——
            10

Equation at the end of step  1  :

   18      2                 31
  (—— -  (—— • (3w - 5))) -  ——  ≤ 0 
   10     10                 10

Step  2  :

            1
 Simplify   —
            5

Equation at the end of step  2  :

   18     1                 31
  (—— -  (— • (3w - 5))) -  ——  ≤ 0 
   10     5                 10

Step  3  :

Equation at the end of step  3  :

   18    (3w - 5)     31
  (—— -  ————————) -  ——  ≤ 0 
   10       5         10

Step  4  :

            9
 Simplify   —
            5

Equation at the end of step  4  :

   9    (3w - 5)     31
  (— -  ————————) -  ——  ≤ 0 
   5       5         10

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 9 - ((3w-5))     14 - 3w
 ————————————  =  ———————
      5              5   

Equation at the end of step  5  :

  (14 - 3w)    31
  ————————— -  ——  ≤ 0 
      5        10

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (14-3w) • 2
   ——————————————————  =   ———————————
         L.C.M                 10     

   R. Mult. • R. Num.      31
   ——————————————————  =   ——
         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:

 (14-3w) • 2 - (31)     -6w - 3
 ——————————————————  =  ———————
         10               10   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -6w - 3  =   -3 • (2w + 1) 

Equation at the end of step  7  :

  -3 • (2w + 1)
  —————————————  ≤ 0 
       10      

Step  8  :

 8.1    Multiply both sides by  10 

 8.2    Divide both sides by  -3 

Remember to flip the inequality sign:

 8.3    Divide both sides by  2  

      w+(1/2)  ≥ 0

Solve Basic Inequality :

 8.4      Subtract  1/2  from both sides

            w ≥ -1/2

Inequality Plot :

 8.5      Inequality plot for

         -0.600 X  - 0.300  ≥  0

  
 

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