ANSWER and EXPLANATION
The measure of angle 1 is greater than 97° and at most 115° (that means less than or equal to)
This means that:
[tex]\begin{gathered} <1\text{ > 97}\degree \\ <1\text{ }\leq\text{ 115}\degree \end{gathered}[/tex]
From the diagram, angle 1 is equal to (9x + 7). This is because they are alternate interior angles.
This therefore means that:
[tex]\begin{gathered} 9x\text{ + 7 > 97}\degree \\ \text{and} \\ 9x\text{ + 7 }\leq\text{ 115}\degree \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} 9x\text{ > 97 - 7} \\ 9x\text{ > 90} \\ \text{Divide through by 9:} \\ x\text{ > 10} \\ \text{and} \\ 9x\text{ }\leq\text{ 115 - 7} \\ 9x\text{ }\leq\text{ 108} \\ \text{Divide through by 9:} \\ x\text{ }\leq\text{ 12} \\ \Rightarrow\text{ 10 < x }\leq12 \end{gathered}[/tex]
Therefore, the number line graph of the possible range of values of x is:
That is the number line.
