Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.5" was replaced by "(65/10)". 2 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 :

                20-((15/10)*x-(65/10))≤0 

Step by step solution :

Step  1  :

            13
 Simplify   ——
            2 

Equation at the end of step  1  :

          15         13
  20 -  ((—— • x) -  ——)  ≤ 0 
          10         2 

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

          3         13
  20 -  ((— • x) -  ——)  ≤ 0 
          2         2 

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:

 3x - (13)     3x - 13
 —————————  =  ———————
     2            2   

Equation at the end of step  3  :

        (3x - 13)
  20 -  —————————  ≤ 0 
            2    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

           20     20 • 2
     20 =  ——  =  ——————
           1        2   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 4.2       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:

 20 • 2 - ((3x-13))     53 - 3x
 ——————————————————  =  ———————
         2                 2   

Equation at the end of step  4  :

  53 - 3x
  ———————  ≤ 0 
     2   

Step  5  :

 5.1    Multiply both sides by  2 

 5.2    Multiply both sides by (-1)

Flip the inequality sign since you are multiplying by a negative number

      3x-53  ≥ 0

 5.3    Divide both sides by  3  

      x-(53/3)  ≥ 0

Solve Basic Inequality :

 5.4      Add  53/3  to both sides

             x ≥ 53/3

Inequality Plot :

 5.5      Inequality plot for

         -1.500 x  + 26.500  ≤  0

  
 

One solution was found :