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# anyone help plez

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Find all x such that \(x^2+5x<6\). Express your answer in interval notation.

Jul 26, 2019

#1
+8966
+3

x2 + 5x  <  6

Subtract  6  from both sides of the inequality.

x2 + 5x - 6  <  0

Let's find what values of  x  make  x2 + 5x - 6  equal  0

x2 + 5x - 6  =  0

Factor the left side. What two numbers add to  5  and multiply to  -6 ?   -1  and  +6

(x - 1)(x + 6) = 0

Set each factor equal to zero and solve for  x

 x - 1  =  0     or     x + 6  =  0 x  =  1                   x  =  -6 Since a graph of   y  =  x2 + 5x - 6  is a parabola, we can be sure that the values of  x  that would make  y < 0  fall in one of these two intervals: either   the interval  (-6, 1)   or   the interval  (-∞, -6) U (1, ∞) To determine which interval is the solution set, let's test a number in both of them. 0  is a number in the interval  (-6, 1) If   x  =  0   then   y  =  (0)2 + 5(0) - 6  =  -6 And   -6 < 0   so we know  0  should be included. 2  is a number in the interval  (-∞, -6) U (1, ∞) If   x  =  2   then   y  =  (2)2 + 5(2) - 6  =  8 And  2  > 0   so we know  2  should not be included. So we can be sure that   x2 + 5x - 6  <  0   if and only if  x  is in the interval  (-6, 1)

Jul 26, 2019
#2
+1

thanks hectictar

Jul 27, 2019