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 —>)
The correct graph is option B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 <———•——————————> (red line <—)
To match the inequality to its graph, let's simplify the inequality first:
3 - 2(x + 4) <= 5
Start by distributing the -2:
3 - 2x - 8 <= 5
Combine like terms:
-2x - 5 <= 5
Now, add 5 to both sides:
-2x <= 10
Finally, divide by -2 (remember to reverse the inequality when dividing by a negative number):
x >= -5
Now let's analyze the answer choices:
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line —>)
This represents x > -5, but the inequality is x >= -5. Therefore, it is not a match.
B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
This represents x < -5, which is not correct.
C). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line <—)
This represents x < -5, which is not correct.
D). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line —>)
This represents x >= -5, which matches the inequality x >= -5.
Therefore, the matching graph is option D.
To match the inequality to its graph, we need to solve the inequality first and then analyze the resulting expression.
Let's solve the inequality step by step:
3 - 2(x + 4) <= 5
First, distribute the -2 to the terms inside the parentheses:
3 - 2x - 8 <= 5
Combine like terms:
-2x - 5 <= 5
Next, isolate the variable by moving the constant term to the opposite side of the inequality sign:
-2x <= 5 + 5
-2x <= 10
Finally, divide both sides of the inequality by -2. Since we are dividing by a negative number, we need to flip the inequality sign:
x >= 10 / -2
x >= -5
Therefore, the solution to the inequality is x is greater than or equal to -5.
Now, let's analyze the given graphs:
A). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line —>)
This graph seems to represent x being less than -5, which is the opposite of the solution. So it does not match the inequality.
B). -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
<———•——————————> (red line <—)
This graph seems to represent x being greater than -5, which matches the solution x >= -5. So it is a possible match.
C). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line <—)
This graph seems to represent x being between 0 and 8, which does not match the solution. So it does not match the inequality.
D). 0-|-|-|-|-|-|-| 8 -|-|-10
<—————o———> (red line —>)
This graph seems to represent x being greater than 8, which is the opposite of the solution. So it does not match the inequality.
Based on the analysis, the match for the inequality 3 - 2(x + 4) <= 5 is B) -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 and <———•——————————> (red line <—).