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Solution - Adding, subtracting and finding the least common multiple

x \geq \frac{96}{5}

x>=96/5

Step by Step Solution

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.4" was replaced by "(24/10)".

Rearrange:

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

x/(-8)-(-(24/10))≤0

Step by step solution :

Step 1 :

            12
 Simplify   ——
            5

Equation at the end of step 1 :

   x          12
  —— -  (0 -  ——)  ≤ 0 
  -8          5

Step 2 :

             x
 Simplify   ——
            -8

Equation at the end of step 2 :

   x    -12
  —— -  ———  ≤ 0 
  -8     5

Step 3 :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

      The left denominator is :       -8

      The right denominator is :       5

Number of times each prime factor
appears in the factorization of:
Prime Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
2	3	0	3
5	0	1	1
Product of all Prime Factors	-8	5	40

Least Common Multiple:
40

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 = -5

   Right_M = L.C.M / R_Deno = 8

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.      x • -5
   ——————————————————  =   ——————
         L.C.M               40  

   R. Mult. • R. Num.      -12 • 8
   ——————————————————  =   ———————
         L.C.M               40

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:

 x • -5 - (-12 • 8)     96 - 5x
 ——————————————————  =  ———————
         40               40

Equation at the end of step 3 :

  96 - 5x
  ———————  ≤ 0 
    40

Step 4 :

4.1    Multiply both sides by 40

4.2    Multiply both sides by (-1)

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

      5x-96 ≥ 0

4.3    Divide both sides by 5

      x-(96/5) ≥ 0

Solve Basic Inequality :

 4.4      Add  96/5  to both sides

             x ≥ 96/5

Inequality Plot :

 4.5      Inequality plot for

         -0.125 x  + 2.400  ≤  0

One solution was found :

x ≥ 96/5

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