Answer:
<h2>1 < x < 6 ⇒ x ∈ (1, 6)</h2>Step-by-step explanation:
3x - 8 > -5 <em>add 8 to both sides</em>
3x > 3 <em>divide both sides by 3</em>
x > 1
2x - 7 < 5 <em>add 7 to both sides</em>
2x < 12 <em>divide both sides by 2</em>
x < 6
From x > 1 and x < 6 we have the solution 1 < x < 6 ⇒ x ∈ (1, 6)
First we need to know the coordinates of the movie theater, we can do this applying the midpoint formula:
We have that the movie theater is located at (2,4). Now we use this coordinates to find the location of Clara's house using again the midpoint formula:
Therefore, Clara's house is located at (-2,0)