Solving Solving InequalitiesInequalities

Objective:SWBAT solve and graph compound inequalities

Review: Graphing Review: Graphing InequalitiesInequalities

• Open dot: > or <• Closed dot: > or <

• Which direction to shade the graph?oLet the arrow point the way

Note: the variable has to be on the left for this trick to work

Solving Inequalities Solving Inequalities and Graphingand Graphing

7x – 5 < 6x + 4x – 5 < 4x < 9

0-5 9

Interval Notation (-∞, 9)

Solving Inequalities Solving Inequalities and Graphingand Graphing

0-1 1

9

2xx

2xx9

2x10

5

1x 2

Interval Notation (-∞, 1/5 ]

Solving Inequalities and GraphingSolving Inequalities and Graphing

Special Case #1Special Case #1

4(x – 3) < 2(2x – 5)4x – 12 < 4x – 10 – 12 < – 10

• Always true• Infinite solutions• All real #s Interval Notation

(-∞, ∞)

Special case #2Special case #2• 2(3x + 5) > 6(x – 1) + 17• 6x + 10 > 6x – 6 + 17• 6x + 10 > 6x – 6 + 17• 6x + 10 > 6x + 11• 10 > 11• Always false• NO SOLUTION• no value of x works !

COMPOUND INEQUALITIESCOMPOUND INEQUALITIES

“AND” Case“AND” Case

13< 2x + 7< 17 13 < 2x+72x+7<17

3 < x < 5 Interval Notation (3, 5)

x < 5x > 3

COMPOUND INEQUALITIESCOMPOUND INEQUALITIES

“AND” Case“AND” Case

191x320

1913

1320

x

x

6

7

x

x

6x7

-7 0 6Interval Notation [-7, 6)

COMPOUND INEQUALITIESCOMPOUND INEQUALITIES

“OR” case“OR” case

y – 2> -3 or y + 4 < -3 y > -1 y < -7

-5-7 -3 -1

Interval Notation (- ∞,-7) and (-1,∞)

COMPOUND INEQUALITIESCOMPOUND INEQUALITIES

“OR” case“OR” case

4)1x(3 4)3x(2

43x3 46x2 1x3 10x2

5x 3

1x

OR

Interval Notation (-∞, ∞)