1.4 Solving Inequalities

Review: Graphing Inequalities

• Open dot:> or <• Closed dot: > or <

• Which direction to shade the graph?– Let the arrow point the way

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

Solving Inequalities and Graphing

7x – 5 < 6x + 4x – 5 < 4x < 9

0-5 9

Interval Notation (-∞, 9)

Solving Inequalities and Graphing

0-1 1

9

2xx

2xx9

2x10

5

1x 2

Interval Notation (-∞, 1/5 ]

Solving Inequalities and Graphing

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

All realsInterval Notation (-∞, ∞)

Ex- special 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

• NO SOLUTION

• - no value of x works !

COMPOUND INEQUALITIES“AND” Case

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

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

x < 5x > 3

COMPOUND INEQUALITIES“AND” Case

191x320

1913

1320

x

x

6

7

x

x

6x7 -7 0 6

COMPOUND INEQUALITIES“OR” case

y – 2> -3 or y + 4 < -3 y > -1 y < -7

-5-7 -3 -1

Interval Notation (- ∞,-7) and (-1,∞)

COMPOUND INEQUALITIES“OR” case

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

43x3 46x2 1x3 10x2

5x 3

1x

OR

Interval Notation: All real numbers