Question
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Answer
Here’s how to graph each inequality on a number line:
-
For
: - Draw an open circle at 4 and shade to the right.
-
For
: - Draw a closed circle at 8 and shade to the right.
-
For
: - Draw an open circle at
and shade to the left.
- Draw an open circle at
-
For
: - Draw a closed circle at
and shade to the left.
- Draw a closed circle at
Solution
-
For
: - The solution consists of all numbers greater than 4.
- On the number line, place an open circle at 4 (since 4 is not included) and shade the part to the right.
-
For
: - The solution consists of all numbers greater than or equal to 8.
- On the number line, place a closed (filled) circle at 8 (indicating 8 is included) and shade the part to the right.
-
For
: - The solution consists of all numbers less than
. - On the number line, place an open circle at
and shade the part to the left.
- The solution consists of all numbers less than
-
For
(which is equivalent to ): - The solution consists of all numbers less than or equal to
. - On the number line, place a closed (filled) circle at
and shade the part to the left.
- The solution consists of all numbers less than or equal to
Answered by UpStudy AI and reviewed by a Professional Tutor
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Mind Expander
To graph the inequality
, first, solve for
:
This means
is any value greater than
. On the number line, you would draw an open circle at
and shade to the right to indicate all the values greater than
.
For the inequality
, place a closed circle at 8 on the number line, indicating that 8 is included in the solution set. Shade to the right to represent all numbers greater than or equal to 8.
When graphing
(about 0.22), draw an open circle at
and shade to the left to indicate all values less than
.
Lastly, for
, draw a closed circle at -3 and shade to the left as it includes all numbers less than or equal to -3.
Now you have a colorful number line representation of these inequalities!