Question

The target temperature for a laboratory is 72 ° Fahrenheit. It can vary by up to 2 °. If t is the temperature in the laboratory, which of the following inequalities represents this situation?

1) t - 72 ≤ 2
2) t - 2 ≤ 72
3) t + 2 ≤ 72
4) t - 72 ≥ 2

Answer 1

The correct inequality representing the laboratory temperature that is 72 °F with an allowable variation of ±2 °F is t - 72 ≤ 2. This accounts for temperatures between 70 °F and 74 °F.

Step-by-step explanation:

The laboratory's target temperature is set to 72 °F with a permissible variation of up to 2 °F. This means the temperature, represented by t, can be 2 °F higher or lower than the target temperature. Mathematically, this is expressed as an inequality: 70 °F ≤ t ≤ 74 °F, where t must be equal to or greater than 70 °F and equal to or less than 74 °F. Rewriting the inequality by isolating t leads to two separate inequalities: t ≥ 72 °F - 2 and t ≤ 72 °F + 2. Hence, the correct inequality representing the situation is option 1: t - 72 ≤ 2.