1.7, 2.1 Equations and Inequalities Involving Absolute Values (Linear) & The Coordinate Plane

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9 Terms

1
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absolute value

|x|=a means x=-a or x=a

|x|< a means -a

2
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solving an equation/inequality with one absolute value

1. isolate the absolute value

2. get rid of the absolute value

3. solve the obtained equations/inequalities

<p>1. isolate the absolute value</p><p>2. get rid of the absolute value</p><p>3. solve the obtained equations/inequalities</p>
3
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solving |x+4| = -5

has no solution because the inequality must always be greater than zero

4
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solving |x+7| > -5

since must be |x+7|>=0, the solution will be

(-infinity, infinity)

5
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intersections and unions

and=intersection

or=union

<p>and=intersection</p><p>or=union</p>
6
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coordinate plane

a plane in which a horizontal number line and a vertical number line intersect at their zero points

<p>a plane in which a horizontal number line and a vertical number line intersect at their zero points</p>
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coordinates

Ordered pairs that identify points on a coordinate plane. (x,y)

<p>Ordered pairs that identify points on a coordinate plane. (x,y)</p>
8
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midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

<p>(x₁+x₂)/2, (y₁+y₂)/2</p>
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Distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

OR think of distance between two points as the hypotenuse of a right triangle

use pythagorean theorem

<p>d = √[( x₂ - x₁)² + (y₂ - y₁)²]</p><p>OR think of distance between two points as the hypotenuse of a right triangle</p><p>use pythagorean theorem</p>