i need help solving 2x^2+x<=6

Question

I dont know the interval notations all my answer I come up with are incorrect

Answer 1

2x² + x ≤ 6

 

2x² + x - 6 ≤ 0

 

Factors to:

 

(2x-3)(x+2) ≤ 0

 

This is equal to or less than zero when:

• one of the factors is zero
• one factor is negative and the other positive

 

(2x-3) ≤ 0 for x ≤ 3/2

 

(x+2) ≤ 0 for x ≤ -2

 

Below -2, both factors are negative.  Above 3/2, both factors are positive.  Only in between -2 and 3/2 (inclusive) is one factor positive and the other negative or zero.  So the answer is:

 

-2 ≤ x ≤ 3/2

 

In interval notation:

 

[-2, 3/2]

Answer 2

Destiny,

 

2x²+x<=6  ------- this is a parabola that opens up, which means when you find the x-intercepts

                           they will be the boundary with in which the inequality is satisfied 

2x²+x-6<=6-6

2x²+x-6<=0

2x²+2x-3x-6<=0

2x(x+2)-3(x+2)<=0

(2x-3)(x+2)<=0

The zeros are 3/2 and -2 and, as stated above, the solution is satisfied when the x values are between the two, boundaries included. 

[-2,3/2]

If you can't see the boundaries, evaluate the function for x=-3, 0 and 3 and that will help you see

 

I hope this helps