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lexussmi12
X+10/X+3 <2 The x+10 is over x+3 but that is a little hard to do on a computer. but all of the is less then < 2 I need to see how it's done...I am not getting this. Thank you for any help!
NVM Multiply both sides of the inequality by (x+3). You should then have x+10 <2(x+3) Distribute the 2...........you should get x+10 < 2x+6 Subtact x from both sides......... 10 < x+6 Subtact 6 from both sides......... 4 < x In interval notation, usually used for inequalities the answer is (4, infinity)
@lexus, sorry the above is not correct. the rational expression has to be related to 0 not 2. the answer is \[(-\infty,-3)\cup(4,\infty)\]METHOD: bring the 2 to the left and get common denominator; write as a simplified rational expression:\[\frac{x+10}{x+3}-2*\frac{x+3}{x+3}<0\]distributing the -2 and combine the fractions\[\frac{x+10-2x-6}{x+3}<0\]simplify the numerator\[\frac{4-x}{x+3}<0\]the rational expression can change sign at the zeros of the numerator and the denominator, i.e., at x=-3 and x=4. you have to check a test point in each the there intervals (see sketch) to check the sign. wherever the expression is negative is an interval of the solution set. Notice that if you pick a test point to the left of -3, such as -4, and evaluate the sign of the numerator and denominator, the fraction is negative. this also happens when you pick test point to the right of 4, such as 5. however, she you pick a test point between -3 and 4 such as 0, the fraction is positive.
here is a sign chart that shows the signs of the factors|dw:1315865230318:dw|
here is a graph of the inequality written as if it were a function showing that it is negative to the left of -3