The graph of the inequality is drawn by placing a shaded circle at 4 as the starting point of ray pointing towards negative infinity
The students that created inequalities with appropriate solution set are;
A. Amanda
D. Diana
Reasons:
Question: The table of the question is presented as follows, and the graph of the inequality is attached
[tex]\begin{array}{|l|l|}\mathbf{\underlie{Amanda}}&-3\cdot x + 5 > -7\\&\\\mathbf{\undrline{Briana}}& \dfrac{1}{2} \cdot (2\cdot x - 4) >2 \\&\\\mathbf{\undrline{Courtney}}&-7\cdot x + 8 > -3 \cdot x +24\\&\\\mathbf{\undrline{Diana}}&9\cdot x - 6 <3 \cdot x+18\end{array}\right][/tex]
Solution:
The inequality with the same solution as the given graph is x < 4
The inequalities created by the students are;
Amanda;
-3·x + 5 > -7
Rearranging the above inequality gives;
-3·x + 5 - 5 > -7 - 5
-3·x > -12
Dividing both sides by (-1) and reversing the inequality sign gives;
[tex]\dfrac{-3 \cdot x}{-3} = x < \dfrac{-12}{-3} = 4[/tex]
x < 4
Therefore;
Briana;
The solution set created by Briana is [tex]\dfrac{1}{2} \cdot (2\cdot x - 4) >2[/tex]
Multiplying both expressions on either side of the equality by 2 gives;
[tex]2\times \dfrac{1}{2} \cdot (2\cdot x - 4) >2\times 2[/tex]
(2·x - 4) > 4
2·x > 4 + 4 = 8
[tex]x > \dfrac{8}{2}[/tex]
Therefore
x > 4
Courtney;
The inequality created by Courtney is -7·x + 8 > -3·x + 24
Rearranging gives;
8 - 24 > -3·x + 7·x
-16 > 4·x
4·x < -16
[tex]x < \dfrac{-16}{4}[/tex]
x < -4
Diana;
Diana's solution is 9·x - 6 < 3·x + 18
Rearranging, we get;
9·x - 3·x < 18 + 6
6·x < 24
[tex]x < \dfrac{24}{6}[/tex]
x < 4
Therefor;
Therefore, the students that created inequalities with appropriate solution set are;
A. Amanda
D. Diana
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