Can anyone please explain how to solve the following inequality?

Distribute the x on the left and square the right side. So then it would be

3x^2 + 2x > x^2 + 4x + 4

subtract x^2 and 2x from both sides

2x^2 > 2x + 4

factor a 2 from 2x + 4

2x^2 > 2(x + 2)

divide by 2 on both sides

x^2 > x + 2

subtract an x and a 2

x^2 - x - 2 > 0

factor

(x-2)(x+1)>0

x>2 or x>-1

so I guess you could write it as -1<x>2

hope I helped!!

it is easy.

to prove the inequality, simplify both these.

x(3x + 2) > (x + 2)^2

3x^2+2x > x^2 + 4 +4x

2x^2 - 2x > 4

2x(x-1)>4

let x = 2

both are equal.

x = 3

equation satisfies inequality.

hence for every value of x above 2 , inequality occurs

solve it as a quadratic first

and then test the 3 parts that the answers can give

by first testing the middle part.

if it doen't fit the bill, the other 2 will

the quadratic will yield the solution (-1,2)

<------ | ------------- | -------->

. . . .-1 . . . . . . . 2

the middle part on testing doesn't fit, so

ans: x < -1 or x > 2

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