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Solution - Adding, subtracting and finding the least common multiple

x < \frac{23}{88}

x<23/88

Step by Step Solution

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 than sign from both sides of the inequality :

-(88/10)*x-(-(23/10))>0

Step by step solution :

Step 1 :

            23
 Simplify   ——
            10

Equation at the end of step 1 :

         88                23
  (0 -  (—— • x)) -  (0 -  ——)  > 0 
         10                10

Step 2 :

            44
 Simplify   ——
            5

Equation at the end of step 2 :

         44          -23
  (0 -  (—— • x)) -  ———  > 0 
         5           10

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       5

      The right denominator is :       10

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
5	1	1	1
2	0	1	1
Product of all Prime Factors	5	10	10

Least Common Multiple:
10

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.      -44x • 2
   ——————————————————  =   ————————
         L.C.M                10   

   R. Mult. • R. Num.      -23
   ——————————————————  =   ———
         L.C.M             10

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:

 -44x • 2 - (-23)     23 - 88x
 ————————————————  =  ————————
        10               10

Equation at the end of step 3 :

  23 - 88x
  ————————  > 0 
     10

Step 4 :

4.1    Multiply both sides by 10

4.2    Multiply both sides by (-1)

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

      88x-23 < 0

4.3    Divide both sides by 88

      x-(23/88) < 0

Solve Basic Inequality :

 4.4      Add  23/88  to both sides

             x < 23/88

Inequality Plot :

 4.5      Inequality plot for

         -8.800 x  + 2.300  >  0

One solution was found :

x < 23/88

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