VOCABULARY
What does ≥ mean?
It means greater than or equal to.
What does ≤ mean?
It means that is it less than or equal to.
What is an easy way to tell if it’s a greater than or less than symbol?
If it is a greater than sign then the pointy end is away from the first
number. If it is a less than sign then the pointy end is pointing towards
the first number.
You could also think of it as the greater than symbol is trying to eat the
first number and the less than symbol is trying to eat the second
number.
GRAPHING
How do you know when or when not to shade in the circle?
When the inequality symbol is “greater than” or “less than”, the circle is
not filled in. When the inequality symbol is “greater than or equal to”
or “less than or equal to,” the circle is filled in.
Another way to see if the circle needs to be filled in is by asking if the
number that has the circle could be a possible answer. If it could be a
possible answer then it is filled in, if not then it is left open.
Why does the direction of the shading matter?
The direction of the shading shows where all the possible values of the
variable are located on the number line. If a value that makes the
statement true is shaded in then you have shaded in in the correct
direction.
Where does the dot go on the graph?
The dot on the graph goes on the value on the other side of the
inequality from the variable. This only works when the variable is by
itself.
ADDING AND SUBTRACTING
What are the rules for subtracting and adding to both sides of an
inequalities?
When adding and subtracting on both sides of an inequality, you must
make sure that you are adding or subtracting the same number just like
when you work with an equation. The inequality symbol will stay the
same regardless of whether you are adding or subtracting or if you are
using a positive or a negative number.
Do you flip the sign when adding or subtracting on both sides of an
inequality?
You do not flip the sign when adding or subtracting on both side of an
inequality. You only flip the sign when you multiply or divide by a
negative number.
MULTIPLYING AND DIVIDING
How do you know if the sign flips?
You know the sign flips if you are multiplying or dividing by a negative
number on both sides of the inequality.
What happens when you divide by a negative?
When you divide both sides of an inequality by a negative number, the
inequality flips. This was shown when we did our walker activities and
Walker A and Walker B walked past each other when they were
multiplied or divided by a negative number.
SOLVING
Why do you have to do the same operation on both sides of the
inequality?
Like an equation, you have to do the same operation on both side of
the inequality to keep it balanced.
Do you have to simplify before you solve?
You should always simplify before you solve. If you don’t, you will end
up doing extra work which gives you more opportunities to make
mistakes.
How do you check the answer for an inequality problem?
To check the answer for an inequality problem, you plug in a value that
you know is true for you final step where the variable is alone on one
side of the inequality and there is just a number on the other side. You
then take that number and plug it in to the original inequality. If it
makes a true statement, then your answer is correct.