Question

1. the difference between the monthly high and low temperatures was less than 27° fahrenheit. the monthly low temperature was -2° fahrenheit. determine the possible monthly high temperature. then interpret the solution. (example 2)

Explanation:

Step1: Define the variable

Let \( h \) be the monthly high temperature (in \( ^\circ\text{F} \)).

Step2: Set up the inequality

The difference between high and low temperatures is \( h - (-2) \) (since low temperature is \( -2^\circ\text{F} \)), and this difference is less than \( 27^\circ\text{F} \). So the inequality is:
\[
h - (-2) < 27
\]

Step3: Simplify the inequality

Simplify \( h - (-2) \) to \( h + 2 \), so the inequality becomes:
\[
h + 2 < 27
\]

Step4: Solve for \( h \)

Subtract 2 from both sides of the inequality:
\[
h + 2 - 2 < 27 - 2
\]
\[
h < 25
\]

Answer:

The possible monthly high temperature \( h \) satisfies \( h < 25^\circ\text{F} \). This means the monthly high temperature must be less than \( 25^\circ\text{F} \) so that the difference between the monthly high and low temperatures (which is \( h - (-2)=h + 2 \)) is less than \( 27^\circ\text{F} \).