Absolute value equation
An equation that contains an absolute value expression
|X| = 4
Distance away from zero
Solve |X|=7
The distance between X and 0 is 7
The solutions are 7 and -7
Solve |X-3| = 8
Rewrite the absolute value equation as 2 equations.
Then solve each equation separately.
1. |X-3|=8 - rewrite original equation.
2. X-3=8 or X-3=-8 - put into two logical cases. Then add three to both.
3. X=11 or X=-5 - the answers are 11 or -5. This is a
OR case
Occurs when the inequality is set to be less than
Compound AND case
When the inequality is set to be greater than
How to decide of an equation can be solved
The absolute value of a number is never set to be negative. When an absolute value expression equals a negative number, there are no solutions. All possible work must be done to isolate the absolute value before this can be determined.
Solve 3|2x-7|-5=4
Rewrite the equation in the form of Ax+By=C
1. 3|2x-7|-5=4 - write original equation.
2. 3|2x-7|=9 - add 5 to both sides
3. |2x-7|=3 - divide by three on both sides
Then, solve the absolute value equation.
1. 2x-7=3 - write absolute value equation.
2. 2x-
Solve and graph an inequality in one variable
Number line.
-2x+3<=9
Solve and graph a linear inequality in 2 variables
Coordinate plane.
Graph of an inequality
Set of points that represent all solutions of the inequality
Open circle
The inequality isn't set equal to anything. > or <
When dividing by a negative number
Reverse inequality symbol
Closed circle
The inequality is set equal to something. >= or <=
When an absolute value opens narrower than f(x)=x
Vertical stretch
When absolute value graph opens wider than f(x)=x
Vertical shrink
Horizontal line/ slope
x=o
Slope is zero
Vertical line/ slope
y=o
Slope is undefined
Dashed line
If not set equal
Solid line
Set equal
How to check if an inequality is true or false
Plug in a value not on the boundary line.
(0,0) is a good starting point.
Boundary line
Line of an inequality equation on a graph with either a dashed or solid line.
Vertex
End point
M
Slope
B
Y intercept
Has to be written as (x,y)
Standard form
Ax+By=C.
If an equation is in this form, the best way to solve and graph if is by using intercepts
Slope intercept form
Y=mx+b
For most equations that need to be graphed, put in this form