Question

grade 8 unit 7
general mathematics (standards)
name

symbols of inequalities: formative assessment

1. there are two thermometers below. write two inequality statements to describe the relationship between the two thermometers.

1. brian has a checkbook balance of -$23.43, and kristen has a checkbook balance of -$18.42. write a statement of inequality to represent the situation. who owes more money, brian or kristen?

Explanation:

Question 1

Step1: Determine temperatures

First, identify the temperatures from the thermometers. Let's say the first thermometer (left) shows a temperature of $-6$ (assuming the level is at -6) and the second (right) shows $-4$.

Step2: Write inequalities

For two numbers \(a\) and \(b\), if \(a < b\), then \(b > a\). So if the first temperature \(T_1=-6\) and the second \(T_2 = - 4\), we can write \(T_1T_1\) (i.e., \(-4>-6\)).

Step1: Recall negative number meaning

A negative checkbook balance means the person owes money. A more negative balance means owing more. Brian's balance: \(-\$23.43\), Kristen's: \(-\$18.42\).

Step2: Compare negative numbers

For negative numbers, the one with the larger magnitude (more negative) is smaller. So \(-23.43<-18.42\) (since \(23.43 > 18.42\), so \(-23.43\) is less than \(-18.42\)). Since a lower (more negative) balance means owing more, Brian owes more.

Answer:

If the first thermometer's temperature is \(T_1\) and the second is \(T_2\), and \(T_1=-6\), \(T_2 = - 4\), the inequalities are \(\boldsymbol{-6 < - 4}\) and \(\boldsymbol{-4 > - 6}\) (values depend on actual thermometer readings, this is a sample based on typical scale interpretation).

Question 2