a. Gabriel is trying to plan his birthday party. At Putt Putt Palace, it is \( \$ 250 \) to rent the facility and \( \$ 7 \) per person that attends. At Mini Golf Madness, it is \( \$ 280 \) to rent the facility and \( \$ 5 \) per person. How many people could Gabriel invite that would be the same price for each place?

\[ \begin{array}{l}|x+6| \leq 7\end{array} \] Solve the absolute value inequality. A. The solution set in interval notation is (Simplify your answer.) The solution set is \( \varnothing \).

7. \( \begin{aligned} y & =2 x+8 \\ y & =-2 x\end{aligned} \)

Determine whether the following equation defines \( y \) as a function of \( x \). \[ x^{2}+y=49 \] Does the equation \( x^{2}+y=49 \) define \( y \) as a function of \( x \) ? Yes No

\[ 11^{-x-4}=4^{3 x} \] Write the exact answer using either base-10 or base-e logarithms. \( x=\square \)

Solve the absolute value inequality. \( |x-6| \geq 1 \) A. The solution set in interval notation is (Simplify your answer.) B. The solution set is \( \varnothing \).