Pre-calculus; linear inequalities

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SUMMARY

The discussion focuses on solving quadratic inequalities, specifically the equations 9x² + 12x + 4 ≥ 0 and 2 - 5x - 3x² ≤ 0. Participants clarify that the first inequality can be factored into (3x + 2)(3x + 2), while the second requires correction as it was misrepresented. The distinction between linear and quadratic inequalities is emphasized, with the latter being the correct classification for the problems presented.

PREREQUISITES
  • Understanding of quadratic equations and their properties
  • Familiarity with factoring polynomials
  • Knowledge of inequality notation and solutions
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the methods for solving quadratic inequalities
  • Learn about the graphical representation of quadratic functions
  • Explore the concept of sign charts for inequalities
  • Review the differences between linear and quadratic inequalities
USEFUL FOR

Students studying pre-calculus, educators teaching algebraic concepts, and anyone seeking to improve their skills in solving quadratic inequalities.

priscilla98
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Homework Statement



1. 9x^2 + 12x + 4 ≥ 0

2. 2 - 5x - 3x^2 ≤ 0

Homework Equations



The Attempt at a Solution



1. Can't you factor this into (3x + 2) (3x + 2)?
2. Looking at this inequality, I am thinking if you can change this inequality into 3x^2 + 5x + 2.
 
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priscilla98 said:

Homework Statement



1. 9x^2 + 12x + 4 ≥ 0

2. 2 - 5x - 3x^2 ≤ 0

Homework Equations



The Attempt at a Solution



1. Can't you factor this into (3x + 2) (3x + 2)?

Yes, you can. So what is your conclusion about the x that satisfy it?

2. Looking at this inequality, I am thinking if you can change this inequality into 3x^2 + 5x + 2.

What you have changed it into isn't an inequality and you likely have a sign error. Did you mean to write 3x2 + 5x - 2 ≥ 0? If so, what next?

Also, your title says linear inequalities. These aren't linear inequalities; they are quadratic inequalities.
 

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