OCF.01.1 - Inequalities

MCR3U - Santowski 1

(A) Review

 (i) Symbols: Inequalities make use of the following symbols: >, >, <, < (meaning either less than, greater than or equal to)  (ii) Interpretation: greater than 8 ex. 3 x - 1 > 8 is an inequality that reads 3 x - 1 is  (iii) Techniques: In working with inequalities, the regular rules for equations hold true => what ever you do to one side of the equation, you must do to the other side of the equation.  Only one variation in techniques will be reviewed => when multiplying or dividing through by a negative quantity, reverse the inequality symbol 2

(A) Review

 (iv) Solutions: In solving an inequality, we are looking for every possible value for x that satisfies the given condition. As such, there will be many possible values for the variable (unlike linear or quadratic equations)  (v) Notation: Solutions may be presented using set notation, number lines, or interval notation     (vi) Ex of Set Notation: { { { x x x | x > -2, | 2 < E R | x x x E R} < 7, x E R} < -2}   which becomes [-2, +∞) in interval notation  which becomes (2,7] in interval notation which becomes (-∞, -2] in interval notation  Ex of Number Lines (Draw on board) 3

(B) Examples

 ex 1 Graph each set on a number line     (a) { x (b) { x E N | -5 < x E R | -5 < x < 2} < 2} (c) { x E R | x 2 < 16} (d) { x E R | x 2 > 9} 4

(B) Examples

 ex 2 Solve each inequality and present the solution on a number line, in set notation, and in interval notation    (a) 1 x < -3 (b) 2 a /3 + 4 > 2 (c) -4 < (1 - 3 x )/2 < 1  ex 3 Given a graph of y = 3 x - 1. If the values for x (the domain) are between -2 and 7 ie [-2,7], what values are there for y (called the range).

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(C) Internet Links

   (i) http://www.math.armstrong.edu/MathTutorial/exerciseSt atements/LinearInequalities/LinearInequalities.html

(ii) http://www.purplemath.com/modules/ineqsolv.htm

(iii) http://www.wtamu.edu/academic/anns/mps/math/mathl ab/beg_algebra/beg_alg_tut18_ineq.htm

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(D) Homework

Nelson text p245, Q1bdghi, 2def, 3acdefh, 4,5bc 7