The temperatures on the surface of Mars in degrees Celsius approximately satisfy the inequality |C + 84 | ≤ 6. What range of temperatures corresponds to this inequality?

Key Concepts

Absolute Value Inequality

An absolute value inequality expresses a condition where the distance of a variable from a certain value is constrained within a specific range. In this case, |C + 84| ≤ 6 indicates that the expression C + 84 must lie within 6 units of 0, leading to two separate linear inequalities to solve.

Solving Linear Inequalities

Solving linear inequalities involves isolating the variable to find the range of values that satisfy the inequality. This process often requires breaking down the absolute value inequality into two parts, which can then be solved separately to determine the lower and upper bounds of the variable.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses brackets and parentheses to indicate whether endpoints are included or excluded. For example, the solution to the inequality will be expressed in interval notation to clearly show the range of temperatures that satisfy the original condition.