Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "9." was replaced by "(9/1)". 3 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 :

                (7/10)*x+(8/10)*x-((9/1))≥0 

Step by step solution :

Step  1  :

            9
 Simplify   —
            1

Equation at the end of step  1  :

     7      8
  ((——•x)+(——•x))-9  ≥ 0 
    10     10

Step  2  :

            4
 Simplify   —
            5

Equation at the end of step  2  :

     7          4          
  ((—— • x) +  (— • x)) -  9  ≥ 0 
    10          5          

Step  3  :

             7
 Simplify   ——
            10

Equation at the end of step  3  :

     7         4x     
  ((—— • x) +  ——) -  9  ≥ 0 
    10         5      

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 4.2    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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 4.3      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.      7x
   ——————————————————  =   ——
         L.C.M             10

   R. Mult. • R. Num.      4x • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 4.4       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:

 7x + 4x • 2     15x
 ———————————  =  ———
     10          10 

Reducing to Lowest Terms :

 4.5      The above result can still be reduced :

     15x   3x 
     ——— = —— 
     10    2  

Equation at the end of step  4  :

  3x    
  —— -  9  ≥ 0 
  2     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

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

         9     9 • 2
    9 =  —  =  —————
         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 :

 5.2       Adding up the two equivalent fractions

 3x - (9 • 2)     3x - 18
 ————————————  =  ———————
      2              2   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   3x - 18  =   3 • (x - 6) 

Equation at the end of step  6  :

  3 • (x - 6)
  ———————————  ≥ 0 
       2     

Step  7  :

 7.1    Multiply both sides by  2 

 7.2    Divide both sides by  3 

Solve Basic Inequality :

 7.3      Add  6  to both sides

             x ≥ 6

Inequality Plot :

 7.4      Inequality plot for

         1.500 X  - 9.000  ≥  0

  
 

One solution was found :