Absolute Value Inequalities

• Graph the absolute value function then shade above OR below

Solid line…y <, y>

Dashed line…y<, y>Shade above y>, y>

Shade below…y<, y<

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 1:Graph y < |x – 2| + 3

DASHED line

Shade BELOW

slope = 1 Vertex = (2, 3)

2) Absolute Value Inequalities

Example 2:Graph –y + 1 < -2|x + 2|

2) Absolute Value Inequalities

Example 2:Graph –y + 1 < -2|x + 2|

-y < -2|x + 2| - 1

y > 2|x + 2| + 1-y so CHANGE the direction of the inequality

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

Vertex = (-2, 1)Slope = 2Solid line

Shade above

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

y > 2|x + 2| + 1

2) Absolute Value Inequalities

Example 3:Write an equation for the graph below.