Question

inequalities and solutions

1. the temperature in city a is 2°c. let a represent the temperature in city a in degrees celsius. write the equation that represents the temperature in city a. then graph the solution to the equation on the number line.

inequalities and number lines

1. the temperature in city b is less than 2°c. let b represent the temperature in city b in degrees celsius. write an inequality that represents the temperature in city b. then graph the solutions to the inequality on the number line.

1. the temperature in city c is greater than 2°c. let c represent the temperature in city c in degrees celsius. write an inequality that represents the temperature in city c. then graph the solutions to the inequality on the number line.

Explanation:

Step1: Define equation for City A

The temperature equals $2^\circ\text{C}$, so:
$a = 2$

Step2: Graph for City A

On the number line, plot a filled dot at $2$ (since the value is exactly equal to 2) with no arrow, as only the single value is a solution.

Step3: Define inequality for City B

Temperature is less than $2^\circ\text{C}$, so:
$b < 2$

Step4: Graph for City B

On the number line, plot an open dot at $2$ (since 2 is not included) and draw an arrow pointing left (towards smaller numbers) to show all values less than 2.

Step5: Define inequality for City C

Temperature is greater than $2^\circ\text{C}$, so:
$c > 2$

Step6: Graph for City C

On the number line, plot an open dot at $2$ (since 2 is not included) and draw an arrow pointing right (towards larger numbers) to show all values greater than 2.

Answer:

1. Equation: $a = 2$; Graph: Filled dot at position 2 on the number line.
2. Inequality: $b < 2$; Graph: Open dot at position 2, arrow pointing left.
3. Inequality: $c > 2$; Graph: Open dot at position 2, arrow pointing right.