<span><span><span><span>−<span>x2</span></span>−<span>4x</span></span>+5</span>>0</span> Let's find the critical points of the inequality.<span><span><span><span> −<span>x2</span></span>−<span>4x</span></span>+5</span>=0</span><span><span><span> (<span><span>−x</span>+1</span>)</span><span>(<span>x+5</span>)</span></span>=0</span>(Factor left side of equation)<span><span><span><span> −x</span>+1</span>=<span><span><span>0<span> or </span></span>x</span>+5</span></span>=0</span>(Set factors equal to 0)<span><span> x=<span><span>1<span> or </span></span>x</span></span>=<span>−5</span></span> Check intervals in between critical points. (Test values in the intervals to see if they work.)<span> x<<span>−5</span></span>(Doesn't work in original inequality)<span><span><span> −5</span><x</span><1</span>(Works in original inequality)<span> x>1</span>(Doesn't work in original inequality) Answer: −5<x<1
750 because she on average makes 3000 dollars a month, making her monthly profit 750 but if she needs to spend each month a 500 dollar more then she is only making 250 a month multiply 250 by 3 and she made 750
