Question

1. in alaska, the lowest temperature ever recorded is - 80°f and the highest temperature ever recorded is 100°f. write an inequality that represents the range of temperatures in alaska.
2. write and graph an inequality that represents the numbers that are not solutions of x + 4.2 > 12.7.

inequality

1. a) a one - way ticket at a subway costs $2.75. a monthly pass costs $127. for what numbers of rides should you buy the monthly pass?

b) in february, there are exactly 4 weeks. you rode the subway twice each weekday, four times on each of the saturdays and twice on one sunday in february. about how much do you save by using the monthly pass?
spiraled question from chapter 1

1. |4x + 8|+12 = 24

Explanation:

8.

Step1: Let \(t\) be the temperature.

The lowest temperature is \(- 80^{\circ}F\) and the highest is \(100^{\circ}F\). So the inequality is based on the fact that \(t\) must be greater than or equal to the lowest - value and less than or equal to the highest - value.
\(-80\leq t\leq100\)

Step1: First, solve the inequality \(x + 4.2>12.7\).

Subtract \(4.2\) from both sides: \(x>12.7 - 4.2\), so \(x>8.5\).
The numbers that are not solutions of \(x + 4.2>12.7\) are the numbers that satisfy \(x\leq8.5\).

Step2: To graph \(x\leq8.5\) on a number - line:

Draw a closed circle at \(8.5\) (because \(x\) can equal \(8.5\)) and shade to the left of \(8.5\).

Step1: Let \(n\) be the number of rides.

The cost of \(n\) one - way tickets is \(2.75n\). We want to find when \(2.75n\geq127\).
Solve for \(n\) by dividing both sides of the inequality by \(2.75\): \(n\geq\frac{127}{2.75}\approx46.2\).
Since the number of rides \(n\) must be a whole number, \(n\geq47\).

Answer:

\(-80\leq t\leq100\)

9.