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Chapter 1: Problem 77

Identify each as an expression or an equation. \(7 t+2(t+1)=4\)

Short Answer

Expert verified
Equation

Step by step solution

01

Identify Variables and Constants

In the expression, identify all the variables and constants. Here, we have the variable \( t \) and the constants 2, 4, and 7.
02

Check for the Equality Sign

An equation includes an equality sign (\( = \)). Review the given problem to check if it includes one.
03

Conclusion

Since \( 7t + 2(t+1) = 4 \) includes an equality sign, it is an equation.

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Key Concepts

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

Variables
In mathematics, a variable is a symbol used to represent an unknown value. Commonly, letters like \( x \), \( y \), and \( t \) are used. Variables can change, and they are often used in expressions and equations to generalize a mathematical situation. For example, in the equation \( 7t + 2(t+1) = 4 \), the letter \( t \) is a variable. It can take on different values depending on what the equation requires. This flexibility allows us to solve for \( t \) and find its value that makes the equation true. Understanding variables is crucial as they are foundational to algebra and more advanced math topics.
Constants
Unlike variables, constants are fixed values that do not change. In our example equation \( 7t + 2(t+1) = 4 \), the numbers 2, 4, and 7 are constants. These values remain the same regardless of the situation or the variable's value. Constants give an equation or expression its specific form and context. When working with equations, identifying constants is key. They provide the necessary numbers to which the variables relate. Without constants, it would be challenging to set up and solve equations.
Equality Sign
The equality sign (\( = \)) is one of the most important symbols in mathematics. It shows that the values on either side of it are the same. In the equation \( 7t + 2(t+1) = 4 \), the equality sign tells us that whatever the left side equals, it must be the same as the right side value, which is 4. This is what makes the equation an equation and not just an expression. An expression does not include an equality sign. For example, \( 7t + 2(t+1) \) is simply an expression because it lacks an \( = \). Recognizing the equality sign helps us differentiate between equations and expressions, which is crucial in solving mathematical problems.

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Most popular questions from this chapter

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -15,29,8,-6 $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (5 x-2 y)(-2 a) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \left(\frac{5}{6} x+\frac{3}{2} y\right)\left(-\frac{1}{3} a\right) $$

Among entertainment expenditures, the average annual spending per U.S. household on fees and admissions was \(\$ 526\) in 2001 . This amount decreased \(\$ 32\) by 2003 and then increased \(\$ 112\) by \(2006 .\) What was the average household expenditure for fees and admissions in \(2006 ?\)

Simplify each expression. $$ 6(3 p-2)-(5 p+1) $$
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