Inequality.Solve the inequality : 17x + 5 >= -6x^2 .

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve: 17x + 5 >= -6x^2

=> 6x^2 + 17x + 5 >= 0

=> 6x^2 + 15x + 2x + 5 >=0

=> 3x(2x + 5) + 1(2x + 5) >=0

=> (3x + 1)(2x + 5) >=0

This is true if either both 3x + 1 >=0 and 2x + 5 >=0

=> x >= -1/3 and x >=-5/2

=> x >= -1/3

or 3x + 1 =< 0 and 2x + 5 =< 0

=> x =< -1/3 and x =< - 5/2

=> x =< -5/2

The required values of x lie in (-inf. , -5/2]U[-1/3 , inf)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll subtract 17x + 5 both sides:

-6x^2 - 17x - 5 =< 0

We'll multiply by -1:

6x^2 + 17x + 5 > = 0

We'll find the roots of the expression:

6x^2 + 17x + 5  = 0

x1 = [-17 + sqrt(289 - 120)]/12

x1 = (-17 + 13)/12

x1 = -4/12

x1 = -1/3

x2 = -30/12

x2 = -15/6

The expression is positive over the intervals (-infinite ; -15/6) U (-1/3 ; +infinite).

We’ve answered 318,995 questions. We can answer yours, too.

Ask a question