Question

Hiiiiii peoples Solve the inequality 6x^2-x<2 please show all steps

Answer 1

Answer:(3x−2)⋅(2x+1)

Step-by-step explanation:

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".  

STEP

1

:

Equation at the end of step 1

 ((2•3x2) -  x) -  2

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  6x2-x-2  

The first term is,  6x2  its coefficient is  6 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   6 • -2 = -12  

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -1 .

     -12    +    1    =    -11  

     -6    +    2    =    -4  

     -4    +    3    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  3  

                    6x2 - 4x + 3x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   2x • (3x-2)

             Add up the last 2 terms, pulling out common factors :

                    1 • (3x-2)

Step-5 : Add up the four terms of step 4 :

                   (2x+1)  •  (3x-2)

            Which is the desired factorization

Final result :

 (3x - 2) • (2x + 1)