Chapter 6 test Algebra 1

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