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Inequalities
3 different types of Inequalities
Inequality notation
Symbol
Meaning
<
>
<
>
Type of
marking on
the number
line
less than
greater than
less than or
equal to
greater than or
equal to
When graphing inequalities on a number line:
1) Mark the number with an open circle or
closed circle using the chart to the right
2) Shade the number line to the right for
greater than and to the left for less than.
Examples
Give the inequality graphed on the number line.
Give the inequality graphed on the number line.
Graph the inequality
Graph the inequality
x>3
Solve the inequality and then graph your
solution. Remember if you multiply or divide by
a negative number you need to switch the
inequality sign.
Distribute to remove ()
Combine like terms
Subtract or Add to get all the numbers on one
side
Multiply or divide to isolate the x
Then graph your solution on a number line
x < -1
Example:
Solve the inequality and graph your solution.
Solve the inequality and graph your solution.
10x – (4 – 3x) > 9x – 8
Solve the inequality for y and graph the solution.*
Solve the inequality for y and graph the solution.*
*Use the notes on the next page
Review:
Find the slope of the line containing each pair
of points
a) (1, -3) and (-4, 7)
Review:
Find the slope of the line containing each pair
of points
b) (-2, 1) and (2, -2)
Write the equation of the line with:
slope = ½ and passing through the point (4,3)
Write the equation of the line with:
slope = -4 and passing through the point (-3,5)
*Hint use point-slope form y = y1 + b (x - x1)
Graphing Inequalities
Symbol
Meaning
Inequalities are graphed using the
same methods as equations to
determine the position of the line
then you decide if the points on the
line are included in the solution and
if the points above or below the line
are included in the solution. Use the
chart to the right.
<
>
<
>
Graph the equation
y  2 
Type of line
the points on the line are not
included and the solutions
are below the line
the points on the line are not
included and the solutions
are above the line
the points on the line are
included and the solutions
are below the line
the points on the line are not
included and the solutions
are above the line
dashed
dashed
solid
solid
3
x
2
1) the y-intercept is (0,-2)
2) the slope is
3 which equals
2
3 rise

2
run
3) solid line
4) shade below
*Hint – use a point-slope equation
Write the equation for each graph.
Graph the inequality
y 4
2
x
3
Graph the inequality
y  2  2( x  1)
A system of inequalities is graphed just like a single inequality. The solution is the overlapping
shaded region. Write a system of inequalities for the solution shown on each graph.
Sketch a graph showing the solution to each
system.
Sketch a graph showing the solution to each
system.