Respuesta :

manissaha129

Answer:

[tex] \sec( \frac{x}{3} ) + 4 > 2 - \sec( \frac{x}{3} ) \\ 2 \sec( \frac{x}{3} ) > - 2 \\ \sec( \frac{x}{3} ) > - 1 \\ \boxed{y = \sec( \frac{x}{3} )} \\ \boxed{y = - 1}[/tex]

B) is the right answer.

xKelvin

Answer:

B

Step-by-step explanation:

We want to solve the inequality:

[tex]\displaystyle \sec\Big(\frac{x}{3}\Big)+4>2-\sec\Big(\frac{x}{3}\Big )[/tex]

First, we can add sec(x/3) to both sides:

[tex]\displaystyle2 \sec\Big(\frac{x}{3}\Big)+4>2[/tex]

Subtracting 4 from both sides yields:

[tex]\displaystyle 2\sec\Big(\frac{x}{3}\Big)>-2[/tex]

And dividing both sides by 2 yields:

[tex]\displaystyle \sec\Big(\frac{x}{3}\Big)>-1[/tex]

Therefore, we can graph the following two functions:

[tex]\displaystyle y=\sec\Big(\frac{x}{3}\Big)\text{ and } y=-1[/tex]

Where our solutions will be all the intervals where y = sec(x/3) is above the line y = -1.