Question

solve 12+11/6x<-5+3x when x€N​

Answer 1

Answer:

x>6

Step-by-step explanation:

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We think you wrote:

12+11/6x<5+3x

This deals with linear inequalities.

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1 result(s) found

x>6

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Step by Step Solution:

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Rearrange:

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

                    12+11/6*x-(5+3*x)<0  

Step by step solution :

STEP

1

:

           11

Simplify   ——

           6  

Equation at the end of step

1

:

         11          

 (12 +  (—— • x)) -  (3x + 5)  < 0  

         6            

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  6  as the denominator :

          12     12 • 6

    12 =  ——  =  ——————

          1        6    

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 :

2.2       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:

12 • 6 + 11x     11x + 72

————————————  =  ————————

     6              6    

Equation at the end of step

2

:

 (11x + 72)    

 —————————— -  (3x + 5)  < 0  

     6          

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  6  as the denominator :

             3x + 5     (3x + 5) • 6

   3x + 5 =  ——————  =  ————————————

               1             6      

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(11x+72) - ((3x+5) • 6)     42 - 7x

———————————————————————  =  ———————

           6                   6    

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  42 - 7x  =   -7 • (x - 6)  

Equation at the end of step

4

:

 -7 • (x - 6)

 ————————————  < 0  

      6      

STEP

5

:

5.1    Multiply both sides by  6  

5.2    Divide both sides by  -7  

Remember to flip the inequality sign:

Solve Basic Inequality :

5.3      Add  6  to both sides

            x > 6

Inequality Plot :

5.4      Inequality plot for

        -1.167 X  + 7.000  >  0