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Chapter 2: Problem 14

Translate to an inequality. The time of the test was between 45 min and 55 min.

Short Answer

Expert verified
The inequality is \( 45 < t < 55 \).

Step by step solution

01

Define the Variable

Let the variable \( t \) represent the time of the test in minutes.
02

Identify the Range

The time of the test is stated to be between 45 minutes and 55 minutes. This gives us a lower limit of 45 minutes and an upper limit of 55 minutes.
03

Set Up the Inequality

Since \( t \) is between 45 and 55, we can set up the inequality as follows: \( 45 < t < 55 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Definition
In algebra, defining a variable is the first crucial step. A variable is essentially a symbol that stands for a number we do not know yet. In this exercise, we need to represent the time of the test with a variable. Use a letter that makes sense for the context. Here, we choose t to represent the time of the test in minutes. This way, whenever we refer to t, we know it relates to the duration of the test.
Range Identification
Next, we need to identify the range within which the variable falls. The problem states that the time of the test is between 45 minutes and 55 minutes. This information allows us to set the lower and upper limits for the time variable. Let's list the steps:
  • Identify the lower limit: 45 minutes.
  • Identify the upper limit: 55 minutes.
So, t must be more than 45 minutes but less than 55 minutes. Remember to clearly mark these limits to avoid confusion later.
Setting Up an Inequality
The last step involves setting up the inequality. An inequality is a mathematical expression that shows the relationship between two values that are not necessarily equal. Given our variable t and the range identified, we form the inequality like this:
\( 45 < t < 55 \).
Here, the symbol '<' means 'less than,' and since t is between 45 and 55, we use two '<' symbols to show that t lies strictly within this range. Thus, the time of the test is constrained to this inequality, ensuring all conditions are met.

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