Match the inequality to its graph. 3 - 2(x + 4) <= 5
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line —>)
B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
C). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line <—)
D). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line —>)
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
To match the inequality to its graph, we need to simplify the inequality first.
3 - 2(x + 4) <= 5
To simplify, distribute the -2:
3 - 2x - 8 <= 5
Combine like terms:
-2x - 5 <= 5
Now, to solve for x, we need to isolate the variable.
Add 5 to both sides:
-2x <= 10
Divide both sides by -2. Note that when dividing by a negative number, the inequality sign flips:
x >= -5
Now let's analyze the answer choices to find the graph that represents this inequality.
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line —>)
This graph represents a less than inequality and does not match our inequality.
B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
This graph represents a greater than inequality and does not match our inequality.
C). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line <—)
This graph represents a less than inequality and does not match our inequality.
D). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line —>)
This graph represents a greater than or equal to inequality, and it matches our inequality x >= -5.
Therefore, the correct answer is option D.
To determine the correct graph for the given inequality, let's first solve the inequality and then graph it.
Given inequality: 3 - 2(x + 4) <= 5
Step 1: Solve the inequality
Start by simplifying the expression within the parentheses:
3 - 2(x + 4) <= 5
3 - 2x - 8 <= 5
Combine like terms:
-2x - 5 <= 5
Add 5 to both sides of the inequality:
-2x <= 10
Divide both sides by -2. Since you are dividing by a negative number, you need to reverse the inequality symbol:
x >= -5
Step 2: Graph the inequality
Now that we have solved for x, we can graph the inequality on a number line:
The variable x is greater than or equal to -5, which means we will have a filled circle at -5 on the number line. Since the inequality includes the equal sign, we shade the region to the right of -5.
Considering the given options:
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line —>)
This option does not represent the correct graph because it shows a red line moving from left to right (which indicates the values should be less than the boundary), but our inequality states that x should be greater than or equal to -5.
B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
This option does not represent the correct graph because it shows a red line moving from right to left (which indicates the values should be greater than the boundary), but our inequality states that x should be greater than or equal to -5.
C). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line <—)
This option does not represent the correct graph because it shows a red line moving from right to left (which indicates the values should be greater than the boundary), but our inequality states that x should be greater than or equal to -5.
D). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line —>)
This option represents the correct graph because it shows a red line moving from left to right (which indicates the values should be greater than or equal to the boundary), and our inequality states that x should be greater than or equal to -5.
Therefore, the correct answer is option D).