2.4: linear inequalities September 26, 2008

Objectives Understand basic vocabulary related to inequalities Use interval notation Solve linear inequalities symbolically, numerically, and graphically Solve compound inequalities

Vocabulary Inequality: compares two items using, ≤, or ≥. 2x>10 Standard form of linear inequality: ax+b>0. Solution set: values that make an inequality a true statement Compound inequality: two inequalities connected by “and” or “or” x> 5 or x<3 -1<x<0

Interval notation (page 1) Lower boundary: – ( if not equal – [ if equal Upper boundary – ) if not equal – ] if equal x>a –X extends towards ∞ –In interval notation (a, ∞) x<a –X extends towards -∞ –In interval notation (-∞, a)

Interval notation (page 2) x ≥a –X extends towards ∞ –In interval notation [a, ∞) x≤a –X extends towards -∞ –In interval notation (-∞, a] a<x<b –In interval notation (a, b) a≤x≤b –In interval notation [a,b]

Interval Notation (page 3) (a, b) is called an open interval (a, b] or [a, b) is called a half-open interval [a, b] is called a closed interval If ∞ or -∞ is involved, it is an infinite interval.

Symbolic method AKA the algebraic method. Solve the same way you would solve a linear equation, except that if you multiply or divide by a negative, you must switch the direction of the inequality symbol. 2x+1 ≥ 9 -x+1<0 x-2 < x-4 3

Numerical method Use a chart to find the values greater than, less than, and equal to. x+2>3x-1 x-1<x+4 xlr

Graphical solution Imagine your inequality as f(x)>g(x) Graph f(x) and g(x) x+2>2x-1 x>x+1 -2<x+1<5

X-intercept method Rewrite so that f(x)<0. X intercept becomes the turning point for the solution. x+1>2x-5 2x>3x-4

Your assignment page –#2-40 –#44, 48, 64, 68, 86, 88, 98