Learning Outcomes
By the end of this section, you will be able to:
- Use properties of real numbers to simplify expressions
- Solve multi-step equations
- Evaluate absolute value expressions
- Solve absolute value equations
- Solve absolute value inequalities
In Module 2, you learned that the mean of a list of numbers, [latex]x_1,x_2,…,x_n[/latex] was found using the formula
[latex]\large \overline{x} = \frac{\sum_{n}^{i=1} x_i}{n} = \frac{x_1 + x_2 + … + x_n}{n}[/latex]
Suppose a student’s overall grade will be determined by their mean score on four, 100-point exams. The student earned 95, 89, and 88 on the first, second and fourth exams in a class. Their mean score is 85 points, but they have misplaced the third exam and want to know that grade. The unknown score is the solution to the equation
[latex]\large \frac{95+89+ x_3 +88}{4} = 85[/latex].
In statistics, we sometimes need to solve equations or manipulate formulas. In this section we’ll review solving first degree equations like the one above, as well as absolute value equations and inequalities.
Recall for success
Look for red boxes like this one throughout the text. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.
