# x^2 + 2x > 3 -- inequality question

#### Guitarman

##### New member
I'm trying my best to understand these type of questions but I am having some trouble. Here's what I've got:

1) x^2 + 2x > 3

x^2 + 2x - 3 > 0
(x - 1)(x + 3) > 0
1 > x > - 3 => interval: [1,-3] <---solution???

Also I have another one:

2) 3 - |2x + 4| < 1

#### stapel

##### Super Moderator
Staff member
1) Solve the related equality, "x<sup>2</sup> + 2x - 3 = 0", to find the endpoints of the intervals. Then use whatever method you've learned to test the intervals. You want the intervals on which x<sup>2</sup> + 2x - 3 is positive, not negative. (Hint: Look at the graph of x<sup>2</sup> + 2x - 3. Where is it above the x-axis?)

And since this is a strict inequality (that is, no "or equal to"), the endpoints (where the quadratic is equal to zero) cannot be part of the solution.

2) You can add and subtract, giving you:

. . . . .2 < |2x + 4|

Then split this into the two linear inequalities that this absolute-value inequality generates, and solve each.

For instance:

. . . . .1 < |x - 5|

. . . . .|x - 5| > 1

. . . . .x - 5 > 1, so x > 6
. . . . .x - 5 < -1, so x < 4