answer:We can solve this equation by considering the two cases: x-7=x+1 and x-7=-(x+1). For the first case, we have x-7=x+1, which simplifies to -7=1, which is not true. For the second case, we have x-7=-(x+1), which simplifies to 2x=-6, or x=-3. Thus, the equation has boxed{1} distinct solution, which is x=-3.The answer is: 1

answer:First, we find g(5) by plugging in x=5 into the function g(x). g(5) = 2(5) - 1 = 9. Next, we find f(g(5)) by plugging in x=9 into the function f(x). f(g(5)) = (9)^2 + 1 = 81 + 1 = boxed{82}. The answer is: 82

answer:Sally brought 342 pens to her class and there are 44 students, so she gave out a total of 44 * 7 = 308 pens. After giving out 308 pens, Sally has 342 - 308 = 34 pens remaining. She decides to leave half of the remaining pens in her locker, so she leaves 34 / 2 = 17 pens in her locker. Sally takes the rest of the pens home, which is 34 - 17 = 17 pens. Therefore, Sally takes home 17 pens. 17 The answer is: 17

answer:The zoo has x new visitors entering the zoo every hour. The zoo is open for 8 hours in one day, so the total number of visitors in one day is 8 * x. If 80% of the total visitors go to the gorilla exhibit, then the number of visitors going to the gorilla exhibit is 0.8 * (8 * x) = 6.4 * x. We are given that the number of visitors going to the gorilla exhibit in one day is 320, so we can write: 6.4 * x = 320. Dividing both sides by 6.4, we get: x = 50. The value of x is 50. 50 The answer is: 50