Solve the inequality 2x^2 + 4x >= 6

Expert Answers
embizze eNotes educator| Certified Educator

Solve `2x^2+4x>=6 ` :

`2x^2+4x>=6 `

`2x^2+4x-6>=0 `

`2(x^2+2x-3)>=0 ` Since 2>0 we look at the quadratic:

`(x+3)(x-1)>=0 `

For x<-3, the left side is positive.

For -3<x<1 the left side is negative.

For x>1 the left side is positive.

(In each case, try a test value such as x=-4,x=0,x=2)

Thus the solution intervals are `x<=-3 ` or `x>=1 `

In interval notation the solution is `(-oo,-3]uu[1,oo) `

The graph:

justaguide eNotes educator| Certified Educator

Excellent answer, embizze!

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question