Inequality solving helps us determine the possible values that satisfy the given conditions.
In this exercise, we want the average of all five students' scores to be greater than 84 and less than 86. This involves setting up and solving an inequality, which is a form of algebraic manipulation.
Here’s how to solve this step-by-step:
First, set up the inequality for the average scores:
\( 84 < \frac{340 + x}{5} < 86 \)
Next, solve the inequality in two parts:
- First part: \( 84 < \frac{340 + x}{5} \). Multiply both sides by 5: \(420 < 340 + x \). Subtract 340 from both sides: \(80 < x\).
- Second part: \( \frac{340 + x}{5} < 86 \). Multiply both sides by 5: \(340 + x < 430 \). Subtract 340 from both sides: \( x < 90\).
Combining both parts, the resulting inequality is: \( 80 < x < 90 \).
This framework helps us determine the valid scores for the fifth student.