Solve and graph the compound inequality on a number line. b > -4 or less than or equal to -7 Show your work
To solve the compound inequality, we will solve each inequality separately and then combine the results.
1. Solve the inequality b > -4:
To graph this inequality on a number line, we will draw an open circle at -4 and shade to the right of it. This indicates that b can be any value greater than -4, but not equal to -4.
2. Solve the inequality b ≤ -7:
To graph this inequality on a number line, we will draw a closed circle at -7 and shade to the left of it. This indicates that b can be any value less than or equal to -7.
Now, we need to combine the two graphs.
Since the original compound inequality is "b > -4 or b ≤ -7", we combine the two graphs by shading the entire number line to the left of -7 and leaving an open circle at -4.
The combined graph shows that b can be any value less than or equal to -7, or any value greater than -4 (excluding -4).
I'm sorry, but I am unable to draw the graph here. However, you can easily draw it on a piece of paper by following the steps described above.
To solve and graph the compound inequality, we need to break it down into two separate inequalities and then combine their solution sets.
The compound inequality we are given is: b > -4 or b ≤ -7
First, let's solve the inequality b > -4:
To solve this inequality, we need to find all values of b that are greater than -4. Since there are no restrictions on b for this inequality, the solution set is all real numbers greater than -4.
Next, let's solve the inequality b ≤ -7:
To solve this inequality, we need to find all values of b that are less than or equal to -7. The solution set for this inequality is all real numbers less than or equal to -7, which includes -7 and any other value less than -7.
Now, let's combine the two solution sets:
The solution to the compound inequality is the union of the solution sets of both inequalities. In other words, it consists of all the values that satisfy either one of the inequalities.
The solution set for the compound inequality b > -4 or b ≤ -7 is all real numbers greater than -4, including -4, and all real numbers less than or equal to -7, including -7.
To graph this compound inequality on a number line:
1. Mark all real numbers greater than -4 with an open circle.
2. Mark all real numbers less than or equal to -7 with a closed circle.
3. Draw a line segment to connect these two points.
On the number line, the segment will start with an open circle at -4 and end with a closed circle at -7. This covers the full range of numbers that satisfy the compound inequality.
To solve and graph the compound inequality "b > -4 or less than or equal to -7," we will break it down into two separate inequalities: "b > -4" and "b ≤ -7."
1. Solving "b > -4":
To solve this inequality, we need to find all the values of b that are greater than -4.
The solution set for this inequality is any value of b that is to the right of -4 on the number line. To graph it:
Step 1: Draw a number line.
Step 2: Mark -4 with a closed circle (since it is not included).
Step 3: Draw an arrow to the right of the circle to indicate all the values greater than -4.
The graph of "b > -4" will look like this:
-4 -3 -2 -1 0 1 2 3 ...
Step 4: Label the arrow with an open circle ">" to indicate that it does not include -4.
2. Solving "b ≤ -7":
To solve this inequality, we need to find all the values of b that are less than or equal to -7.
The solution set for this inequality is any value of b that is to the left of or equal to -7 on the number line.
Step 1: Continue the number line from the previous graph.
Step 2: Mark -7 with a closed circle (since it is included).
Step 3: Draw an arrow to the left of the circle to indicate all the values less than or equal to -7.
The graph of "b ≤ -7" will look like this:
... -6 -5 -4 -3 -2 -1 0 1 2 -7
Step 4: Label the arrow with a closed circle "≤" to indicate that it includes -7.
3. Combining the graphs:
To combine the two graphs into one, we need to find the values that satisfy either "b > -4" or "b ≤ -7". This would be the union of the two graphs.
The final graph will have a closed circle at -7 and an open circle at -4. The shaded area will be to the left of or equal to -7 and to the right of -4.
... -6 -5 -4 -3 -2 -1 0 1 2 -7
This graph represents the compound inequality "b > -4 or b ≤ -7."