6.3 Solving Compound Inequalities Algebra 6.3 Solving Compound Inequalities

The difference between the words “and” and “or” If your mother tells you to do something, do the words she uses make a difference? “Please take out the garbage and make your bed.” “Please take out the garbage or make your bed.” How many chores do you have if she uses the word “and”? Two. You have to do both chores. How many chores do you have if she uses the word “or”? One. You only have to do one chore or the other.

Compound Inequality (2 types) Two inequalities connected by and or or. And Both inequalities must be true -2 < x ≤ 3 means -2 < x and x ≤ 3 All real numbers greater than -2 and less than or equal to 3. Or Only one inequality must be true x ≤ -4 or x > 2 All real numbers less than or equal to -4 or greater than 2.

Graphs of Compound Inequalities And Look like this: Or Look like this:

Graphs of Compound Inequalities And -2 < x ≤ 3 means -2 < x and x ≤ 3 All real numbers greater than -2 and less than or equal to 3. -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Graphs of Compound Inequalities Or x ≤ -4 or x > 2 All real numbers less than or equal to -4 or greater than 2. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Example Solve: -5 ≤ 2x +3 < 7 -3 - 3 -3 -8 ≤ 2x < 4 2 2 2 -3 - 3 -3 -8 ≤ 2x < 4 2 2 2 -4 ≤ x < 2 -5 -4 -3 -2 -1 0 1 2 3

Example Solve: -2 < -2 - x < 1 +2 +2 +2 0 < - x < 3 +2 +2 +2 0 < - x < 3 -1 -1 -1 0 > x > -3 -3 < x < 0 Rewrite in number line order -5 -4 -3 -2 -1 0 1 2 3

You try Solve: -5 ≤ -2x +3 < 9 -3 - 3 -3 -8 ≤ -2x < 6 -2 -2 -2 -3 - 3 -3 -8 ≤ -2x < 6 -2 -2 -2 4 ≥ x > -3 -3 < x ≤ 4 Number line order -4 -3 -2 -1 0 1 2 3 4 5

Example Solve: 6x – 5 < 7 or 8x + 6 ≥ 46 +5 +5 or -6 -6 6 6 8 8 x < 2 or x ≥ 5 -1 0 1 2 3 4 5 6 7

You try Solve: 3x + 1 ≤ 4 or 2x - 5 > 7 -1 -1 or +5 +5 3 3 2 2 x ≤ 1 or x > 6 -1 0 1 2 3 4 5 6 7

A few together from the HW P. 349 #18, #26, #32

Homework Pg. 349 #18-35, 55-69