Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.75" was replaced by "(175/100)". 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 :

                20-((45/10)+(175/100)*x)≥0 

Step by step solution :

Step  1  :

            7
 Simplify   —
            4

Equation at the end of step  1  :

         45     7
  20 -  (—— +  (— • x))  ≥ 0 
         10     4

Step  2  :

            9
 Simplify   —
            2

Equation at the end of step  2  :

         9    7x
  20 -  (— +  ——)  ≥ 0 
         2    4 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       2 

      The right denominator is :       4 

      Least Common Multiple:
      4 

Calculating Multipliers :

 3.2    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 :

 3.3      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.      9 • 2
   ——————————————————  =   —————
         L.C.M               4  

   R. Mult. • R. Num.      7x
   ——————————————————  =   ——
         L.C.M             4 

Adding fractions that have a common denominator :

 3.4       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:

 9 • 2 + 7x     7x + 18
 ——————————  =  ———————
     4             4   

Equation at the end of step  3  :

        (7x + 18)
  20 -  —————————  ≥ 0 
            4    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

           20     20 • 4
     20 =  ——  =  ——————
           1        4   

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

 20 • 4 - ((7x+18))     62 - 7x
 ——————————————————  =  ———————
         4                 4   

Equation at the end of step  4  :

  62 - 7x
  ———————  ≥ 0 
     4   

Step  5  :

 5.1    Multiply both sides by  4 

 5.2    Multiply both sides by (-1)

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

      7x-62  ≤ 0

 5.3    Divide both sides by  7  

      x-(62/7)  ≤ 0

Solve Basic Inequality :

 5.4      Add  62/7  to both sides

             x ≤ 62/7

Inequality Plot :

 5.5      Inequality plot for

         -1.750 x  + 15.500  ≥  0

  
 

One solution was found :