Explanation:
Why can't I plus x² to each side of the inequality x²+4x > -x² ?
(Note: one adds things; one does not plus them.)
You can easily add x² to both sides here:
(x² + 4x) + x² > (-x²) + x², or
2x² + 4x > 0, or
x² + 2x > 0, or
x(x + 2) > 0.
For this to be true, x > 0 and x+2 > 0; or else x < 0 and x+2 < 0.
Case 1: x > 0 and x+2 > 0.
Rewrite this as x > 0 and x > -2.
This is true for all x > 0.
Case 2: x < 0 and x+2 < 0.
Rewrite this as x < 0 and x < -2.
This is true for all x < -2.
The solution set for the inequality, in interval notation, is then (-∞,-2) ∪ (0,∞).
done its a good question btw ....