SOLUTION: What is the set of all solutions of the inequality x^2 + 2x -3 <= 0 (<= means less than or equal to) ? When I did this problem i took x^2 + 2x -3 <= 0 and factored it so it loo

Algebra ->  Trigonometry-basics -> SOLUTION: What is the set of all solutions of the inequality x^2 + 2x -3 <= 0 (<= means less than or equal to) ? When I did this problem i took x^2 + 2x -3 <= 0 and factored it so it loo      Log On


   

Question 755133: What is the set of all solutions of the inequality x^2 + 2x -3 <= 0 (<= means less than or equal to) ?
When I did this problem i took x^2 + 2x -3 <= 0 and factored it so it looked like (x-1)(x+3)=0. Then I took x-1=0 and x+3=0 and solved for x and got 1 and -3 and got [-3,1]. Would that be correct? If not can you please show me how to do it correctly? Thank you :)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You are than halfway to the complete answer. You found the correct roots.

The intervals formed for the expression of x are these:

(-infinity,-3]
[-3,1]
[1, infinity)

Next, determine in which intervals is the given inequality statement true and which false. You can pick points and perform computation if you wish.
OR
You can use your knowledge of parabola equations.

Easiest to just check the middle interval, between the roots. Try any value within it. As example, try x=0.
0%2A0%2B2%2A0-3%3C=0 Is this true?
0-3%3C=-3%3C=0 TRUE!


Knowing how the parabola works, the other intervals are not part of the solution. Solution is highlight%28-3%3C=x%3C=1%29.