Transcript Document

OCF.01.1 - Inequalities
MCR3U - Santowski
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(A) Review
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(i) Symbols: Inequalities make use of the following symbols: >, >,
<, < (meaning either less than, greater than or equal to)
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(ii) Interpretation: ex. 3x - 1 > 8 is an inequality that reads 3x - 1 is
greater than 8
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(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.
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Only one variation in techniques will be reviewed => when
multiplying or dividing through by a negative quantity, reverse the
inequality symbol
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(A) Review
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(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)
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(v) Notation: Solutions may be presented using set notation,
number lines, or interval notation
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(vi) Ex of Set Notation:
{x | x > -2, x E R}  which becomes [-2, +∞) in interval notation
{x | 2 < x < 7, x E R}  which becomes (2,7] in interval notation
{x E R | x < -2}  which becomes (-∞, -2] in interval notation
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Ex of Number Lines (Draw on board)
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(B) Examples
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ex 1 Graph each set on a number line
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(a) {x E N | -5 < x < 2}
(b) {x E R | -5 < x < 2}
(c) {x E R | x2 < 16}
(d) {x E R | x2 > 9}
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(B) Examples
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ex 2 Solve each inequality and present the solution on a
number line, in set notation, and in interval notation
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(a) 1 - x < -3
(b) 2a/3 + 4 > 2
(c) -4 < (1 - 3x)/2 < 1
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ex 3 Given a graph of y = 3x - 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
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(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
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