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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your inequality step-by-step.
[tex]x(x+2)<x[/tex]
[tex]x^2 + 2x < x[/tex]
Let's find the critical points of the inequality.
[tex]x^2 + 2x = x[/tex]
[tex]x^2 + 2x - x - x[/tex] (Subtract x from both sides)
[tex]x^2 + x = 0[/tex]
[tex]x ( x + 1 ) = 0[/tex] (Factor left side of equation)
[tex]x = 0 |OR| x + 1 = 0[/tex] (Set factors equal to 0)
[tex]x = 0 |OR| x = -1[/tex]
Check intervals in between critical points. (Test values in the intervals to see if they work.)
[tex]x < - 1[/tex] (Doesn't work in original inequality)
[tex]-1 < x < 0[/tex] (Works in original inequality)
[tex]x > 0[/tex] (Doesn't work in original inequality)
So the answer is : [tex]-1 < x < 0[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
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If this helped you, could you maybe give brainliest..?
❀*May*❀
