Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.3" was replaced by "(23/10)". 2 more similar replacement(s)

Rearrange:

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

                (67/10)*z-(23/10)-(-9)≥0 

Step by step solution :

Step  1  :

            23
 Simplify   ——
            10

Equation at the end of step  1  :

    67         23     
  ((—— • z) -  ——) -  -9  ≥ 0 
    10         10     

Step  2  :

            67
 Simplify   ——
            10

Equation at the end of step  2  :

    67         23     
  ((—— • z) -  ——) -  -9  ≥ 0 
    10         10     

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:

 67z - (23)     67z - 23
 ——————————  =  ————————
     10            10   

Equation at the end of step  3  :

  (67z - 23)    
  —————————— -  -9  ≥ 0 
      10        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

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

          -9     -9 • 10
    -9 =  ——  =  ———————
          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 :

 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:

 (67z-23) - (-9 • 10)     67z + 67
 ————————————————————  =  ————————
          10                 10   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   67z + 67  =   67 • (z + 1) 

Equation at the end of step  5  :

  67 • (z + 1)
  ————————————  ≥ 0 
       10     

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  67 

Solve Basic Inequality :

 6.3      Subtract  1  from both sides

            z ≥ -1

Inequality Plot :

 6.4      Inequality plot for

         6.700 X  + 6.700  ≥  0

  
 

One solution was found :