Question

The measure of angle 1 is greater than 97 degrees and at most 115. Graph the possible values of x.

Answer 1

We are given the following:

Angle 1 is greater than 97 degrees and at most 115 degrees

The angle alternate to angle 1 is "(9x +7)"; alternate angles are congruent

Using the information above, we will develop the inequality shown below:

`\begin{gathered} 97^(\circ)10 \\ x>10 \\ \\ \therefore x>10 \end{gathered}`

We will proceed to the second portion of the inequality. We have:

`\begin{gathered} (9x+7)\le115^(\circ) \\ 9x+7\le115 \\ \text{Subtract ''7'' from both sides, we have:} \\ 9x\le115-7 \\ 9x\le108 \\ \text{Divide both sides by ''9'', we have:} \\ (9)/(9)x\le(108)/(9) \\ x\le12 \\ \\ \therefore x\le12 \end{gathered}`

We will combine both inequalities into one. We have it thus:

[tex]\begin{gathered} x>10 \\ x\le12 \\ \text{Combining the inequalities, we have:} \\ 10We will proceed to plot this inequality on the number line as shown below: