How do you solve and write the following in interval notation: $2x^2 - 7x - 4<=0$ ?

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Answer 1 · 2017-04-01T20:21:42

The solution to this inequality is: $[-1/2,4]$ (see explanation for an in-depth process of how to solve the inequality).

We start by assuming $<=$ is an $=$ and solving as such:
$2x^2-7x-4=0$
$(2x+1)(x-4)=0$
$x=-1/2, 4$

These points, $x=-1/2$ and $x=4$ , the solutions to the equation, give us the bounds of the intervals for the inequality.

When $x<-1/2$ , the function $(f(x)=2x^2-7x-4)$ is positive.
When $-1/2<$ $x<4$ , the function is negative.
When $x>4$ , the function is positive.

Since we're looking for where $f(x)<=0$ , the interval of the solution is $-1/2<=$ $x<=4$ , which in interval notation is: $[-1/2,4]$ .

How do you solve and write the following in interval notation: 2x^2 - 7x - 4<=02x^2 - 7x - 4<=0?