Quadratic inequality-interval notation

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SUMMARY

The discussion focuses on solving the quadratic inequality 2x² < -x + 10 and expressing the solution in interval notation. The initial step involves setting the corresponding equation 2x² + x - 10 = 0 to find the boundary solutions. After determining the roots, the solution set is established by testing values in the intervals defined by these roots. The final solution is expressed in interval notation based on the results of these tests.

PREREQUISITES
  • Understanding of quadratic equations and their solutions
  • Familiarity with interval notation
  • Knowledge of testing intervals for inequalities
  • Basic algebraic manipulation skills
NEXT STEPS
  • Learn how to solve quadratic equations using the quadratic formula
  • Study the concept of interval notation in depth
  • Explore methods for testing intervals in inequalities
  • Practice solving various types of inequalities, including polynomial and rational
USEFUL FOR

Students studying algebra, particularly those learning about quadratic inequalities and interval notation, as well as educators looking for teaching resources on these topics.

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quadratic inequality--interval notation..

Homework Statement



2x^2<-x+10
Solve inequality and put into interval notation

Homework Equations



interval notation

The Attempt at a Solution


I don't even know where to start. I set it equal to zero -2x^2-x+10=0
 
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It's fine to start by solving the corresponding equation. The solutions of the equation become "boundaries," if you will, of sets of numbers that are solutions to the inequality. Suppose there are two solutions, a & b, with a < b. Then you would have 3 potential range of numbers to test.

Pick a value less than a and test into the original inequality. If the result is a true statement, then x < a would be in the solution set.

Then pick a number between a and b and test. If it works, then a < x < b is in the solution set.

Finally, pick a number in greater than b. If it works, then x > b is in the solution set.
 

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