Graphing Inequalities
Should the circle be open or closed for the inequality 4 <= x?
Closed
x + 4 < 3
x < -1
2x + 9 > 7
x > -1
x + 3x - 4 < 12
x < 4
Is 4x + 2 = 3 an equation or an inequality?
Equation
Should the circle be open or closed for x > 7?
Open
5x >= -10
x>= -2
6x - 8 <= 10
x <= 3
-2(x - 3) >= 8
x <= -1
What are the differences between equations and inequalities?
Equations have an equals sign and only one solution.
Inequalities have inequality symbols and a solution set.
Which was should the arrow be directed? Towards the positive or the negative numbers?
x > -6
Towards the Positive Numbers
x - 8 <= 16
x <= 24
x / 6 + 7 <= 9
x <= 2
6(5 - 3x) < 24
x > 1/3
What does "solution set" mean?
The set or group of all possible solutions to an inequality.
Which was should the arrow be directed? Towards the positive or the negative numbers?
-14 < -x
Towards the Negative Numbers
x / 6 < -3
x < -18
(x + 5) / 4 > 6
x > 19
(3x - 7) / 2 >= 7
x >= 7
When do you need to flip the inequality symbol?
When you multiply or divide by a negative number.
Which was should the arrow be directed? Towards the positive or the negative numbers?
-3x < 9
Towards the Positive Numbers
-7x > 77
x < -11
-5x / 3 < -10
x > 6
-8(-4x + 2) / 3 < 16
x < 2
What does it mean for the circle on the number line to be open or closed?
A closed circle means that the number under the circle is a possible solution to the inequality. An open circle means that the number under the circle is not a possible solution to the inequality.