Mathematics
Smartsims01
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Solve for x. Enter your answer using grouping symbols. x^2 + 3x < 28

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(1) Answers
Teechris191

x² + 3x < 28 x² +3x -28 < 0 x² - 4x + 7x - 28 < 0 x(x - 4) + 7(x - 4) < 0 (x+7) (x-4) < 0 x = -7, x = 4 Take three critical point, one between -7 and 4, one after 4, and one -7. Put these value in the main equation and see if it is true. (In this case I am taking -8, 0, and 5) 1) x = 5     25 + 15 < 28     40 < 28     This is incorrect. Thus x cannot be more than 4. 2)x = 0 0 + 0 < 28 0 < 28 This is true. Thus x can be between -7 and 4 3) x = -8 64 - 24 < 28 40 < 28 This is incorrect. Thus, x cannot be less -7.   Hence, the correct answer using grouping symbols is  -7 < x < 4 Which means x is between -7 and 4.

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