Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "12.9" was replaced by "(129/10)". 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 :

                -(169/10)-(-(129/10)-z)≤0 

Step by step solution :

Step  1  :

            129
 Simplify   ———
            10 

Equation at the end of step  1  :

        169            129     
  (0 -  ———) -  ((0 -  ———) -  z)  ≤ 0 
        10             10      

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10  as the denominator :

         z     z • 10
    z =  —  =  ——————
         1       10  

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 :

 2.2       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:

 -129 - (z • 10)     -10z - 129
 ———————————————  =  ——————————
       10                10    

Equation at the end of step  2  :

        169     (-10z - 129)
  (0 -  ———) -  ————————————  ≤ 0 
        10           10     

Step  3  :

            169
 Simplify   ———
            10 

Equation at the end of step  3  :

        169     (-10z - 129)
  (0 -  ———) -  ————————————  ≤ 0 
        10           10     

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -10z - 129  =   -1 • (10z + 129) 

Adding fractions which have a common denominator :

 5.2       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:

 -169 - ((-10z-129))     10z - 40
 ———————————————————  =  ————————
         10                 10   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   10z - 40  =   10 • (z - 4) 

Equation at the end of step  6  :

  z - 4  ≤ 0 

Step  7  :

Solve Basic Inequality :

 7.1      Add  4  to both sides

             z ≤ 4

Inequality Plot :

 7.2      Inequality plot for

         z  - 4.000  ≤  0

  
 

One solution was found :