SUMMARY
To solve the quadratic inequality x²-4x+3≤(3x+5)(2x-3), first simplify the inequality by expanding the right side using the FOIL method. This results in the expression x²-4x+3≤6x²-9x+15. Rearranging the terms leads to a standard form quadratic inequality. The critical values, which are the roots of the resulting quadratic expression, can then be determined to analyze the three intervals on x for solutions.
PREREQUISITES
- Understanding of quadratic equations and inequalities
- Familiarity with the FOIL method for binomial multiplication
- Knowledge of critical points and interval testing
- Ability to manipulate algebraic expressions
NEXT STEPS
- Practice solving quadratic inequalities with different coefficients
- Learn about interval testing for inequalities
- Explore the relationship between roots and the sign of quadratic expressions
- Study the graphical representation of quadratic functions and their inequalities
USEFUL FOR
Students studying algebra, particularly those tackling quadratic inequalities, as well as educators looking for examples to illustrate solving techniques in mathematics.