WEEK 10. Systems of equations

$1.6x^2 + 1.2x=<-0.2$

If you want to be more comfort you should multiply 10 at both sides of equation first.

$16x^2 + 12x=<-2$

Now you should put everything in one side.

$16x^2 + 12x + 2=<0$

Here, i choose factoring for solving the inequality:

$(4x+1)(4x+2)=<0$

You should first find the answer for being 0 and then examine upper and lower of that numbers.

4x=-1

x=-1/4

4x=-2

x=-1/2

IN first case if x will be less than -1/4 the equation will be less than 0 and if x will be more than -1/4 the equation will be more than 0.

In second case if x will be less than -1/2 the equation will be negative and if x will be more than it, the equation will be positive.

So the only zone that the equation is negative is between -1/4 and -1/2.

So the answer is: -1/2=<x=<-1/4

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