Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.7" was replaced by "(7/10)". 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 :

                     (1/10)-2*t-((7/10))≥0 

Step by step solution :

Step  1  :

             7
 Simplify   ——
            10

Equation at the end of step  1  :

    1            7
  (—— -  2t) -  ——  ≥ 0 
   10           10

Step  2  :

             1
 Simplify   ——
            10

Equation at the end of step  2  :

    1            7
  (—— -  2t) -  ——  ≥ 0 
   10           10

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

          2t     2t • 10
    2t =  ——  =  ———————
          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 :

 3.2       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:

 1 - (2t • 10)     1 - 20t
 —————————————  =  ———————
      10             10   

Equation at the end of step  3  :

  (1 - 20t)     7
  ————————— -  ——  ≥ 0 
     10        10

Step  4  :

Adding fractions which have a common denominator :

 4.1       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:

 (1-20t) - (7)     -20t - 6
 —————————————  =  ————————
      10              10   

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -20t - 6  =   -2 • (10t + 3) 

Equation at the end of step  5  :

  -2 • (10t + 3)
  ——————————————  ≥ 0 
        10      

Step  6  :

 6.1    Multiply both sides by  10 

 6.2    Divide both sides by  -2 

Remember to flip the inequality sign:

 6.3    Divide both sides by  10  

      t+(3/10)  ≤ 0

Solve Basic Inequality :

 6.4      Subtract  3/10  from both sides

            t ≤ -3/10

Inequality Plot :

 6.5      Inequality plot for

         -2.000 X  - 0.600  ≤  0

  
 

One solution was found :