1.4 solving inequalities. review: graphing inequalities open dot:> or < closed dot:> or...
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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