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Chapter 7: Problem 7

Classify each of the following as either an expression or an equation. $$\frac{t+3}{t-4}=\frac{t-5}{t-7}$$

Short Answer

Expert verified
Equation

Step by step solution

01

Identify the components

First, identify the components of the given mathematical statement. The statement is \(\frac{t+3}{t-4}=\frac{t-5}{t-7}\).
02

Determine if there is an equality sign

Check if the statement contains an equality sign ( = ). If it does, the statement is an equation. If it does not, the statement is an expression.
03

Classify the statement

Since the given statement \(\frac{t+3}{t-4}=\frac{t-5}{t-7}\) contains an equality sign, it is classified as an equation.

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Key Concepts

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

mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operations. An example of an expression is \(\frac{t+3}{t-4}\). In an expression, there is no equality sign (=). These can be as simple as \(2 + 3\) or more complex like \(3x^2 + 4y - 7\). Expressions are used to represent values and can be simplified or evaluated, but they don鈥檛 tell us more beyond that. Understanding expressions is crucial because they form the building blocks for equations.

equality sign
The equality sign (=) is a fundamental part of mathematics. It denotes that two mathematical expressions on either side of it are equal. In our given example, \(\frac{t+3}{t-4} = \frac{t-5}{t-7}\), the equality sign shows that the two expressions have the same value for certain values of t. Recognizing the equality sign is what transforms an expression into an equation. Equations can be solved to find the value of unknown variables, giving them a critical role in problem-solving.

step-by-step solution
Breaking down problems into step-by-step solutions can help simplify complex concepts. Let's revisit the steps from our example:

  • Identify the components: Determine the pieces involved in the statement, specifically products, sums, variables, etc. In our case, the components are fractions involving t+3, t-4, t-5, and t-7.

  • Determine the presence of an equality sign: Checking for the = sign helps to decide if it's an equation or an expression. Here, the sign is present.

  • Classify the statement: Since the statement contains an equality sign, classify it as an equation: \(\frac{t+3}{t-4} = \frac{t-5}{t-7}\).

This methodical approach ensures clarity and understanding, making it easier to handle more complex problems in algebra.

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