Question

write a compound inequality for the following real - world situations. mr. lewis likes to keep his bedroom between 66 and 70 degrees (including those endpoints). if t represents the temperature of his room, write a compound inequality to represent this. 7. the nurse will only keep students in her office if they have a temperature below 97 or above 100 degrees (not including those temps). if x represents a students internal temperature, write a compound inequality to represent this. x + 5 < 3 or - 6x ≤ - 24 9. - 7 < 2x + 1 < 3

Explanation:

Step1: Analyze Mr. Lewis's situation

Since the temperature 't' is between 66 and 70 (inclusive), we use a compound - inequality with less than or equal to signs.
$66\leq t\leq70$

Step2: Analyze the nurse's situation

The temperature 'x' is below 97 or above 100 (exclusive), so we use strict inequality signs.
$x < 97$ or $x>100$

Step3: Solve $x + 5<3$

Subtract 5 from both sides.
$x+5 - 5<3 - 5$
$x<-2$

Step4: Solve $-6x\leq - 24$

Divide both sides by - 6. Remember to reverse the inequality sign when dividing by a negative number.
$\frac{-6x}{-6}\geq\frac{-24}{-6}$
$x\geq4$
The solution is $x < - 2$ or $x\geq4$

Step5: Solve $-7 < 2x+1 < 3$

First, subtract 1 from all parts of the compound - inequality.
$-7-1 < 2x+1 - 1<3 - 1$
$-8 < 2x<2$
Then divide all parts by 2.
$\frac{-8}{2}<\frac{2x}{2}<\frac{2}{2}$
$-4 < x<1$

Answer:

1. $66\leq t\leq70$
2. $x < 97$ or $x>100$
3. $x < - 2$ or $x\geq4$
4. $-4 < x<1$