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Chapter 1: Problem 85

What is the difference between a variable, a variable expression, and an equation?

Short Answer

Expert verified
A variable is a symbol; a variable expression combines variables and numbers; an equation includes an '=' sign.

Step by step solution

01

Define Variable

A variable is a symbol, often a letter, that represents a number in mathematical expressions and equations. For example, in the expression 3x + 2, 'x' is the variable.
02

Define Variable Expression

A variable expression is a mathematical phrase that combines numbers, variables, and operation symbols (+, -, *, /). Unlike equations, variable expressions do not include an equals sign. For instance, 2x + 5 is a variable expression.
03

Define Equation

An equation is a mathematical statement that asserts the equality of two expressions, which includes an '=' sign. For example, 3x + 2 = 11 is an equation, indicating that 3x + 2 is equal to 11.
04

Highlight Differences

The main differences are: a variable is a symbol, a variable expression combines variables and numbers but does not have an '=' sign, and an equation includes an '=' sign and shows the equality between two expressions.

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Key Concepts

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

Variable
To understand variables, picture them as placeholders. They are symbols (often letters like x, y, or z) used to represent unknown numbers. For example, in the expression 4y - 7, the letter 'y' stands for a number that we do not yet know. Variables are extremely useful because they let us write general formulas and solve various problems by substituting different values.
Variable Expression
A variable expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division). These expressions do not have an equals sign. For example, consider the expression 5a + 3. Here, 'a' is a variable and the entire expression represents a value that changes depending on the value of 'a'. Variable expressions are fundamental in creating formulas and solving algebraic problems.
Equation
An equation is like a statement in mathematics that asserts that two expressions are equal. It contains an equals sign (=). For example, 2x + 5 = 15 is an equation. This means that the expression 2x + 5 has the same value as 15. Equations are essential in algebra because they allow us to find the value of unknown variables by solving them.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operation symbols. These expressions do not contain an equals sign. Examples include 7y - 4 and 3a + 2b. Mathematical expressions are the building blocks for creating more complex mathematical statements and are used to represent quantities and relationships in a concise and generalized way.

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Most popular questions from this chapter

Evaluate. $$ 45 \div 3 \cdot a, \text { for } a=-1 $$

Simplify. $$ 5 t^{3}+t+3\left(t-2 t^{3}\right) $$

Translate to an inequality. A number \(x\) is nonpositive.

Evaluate. $$ 9-4 x, \text { for } x=5 $$

If \(n\) is positive and \(m\) is negative, what is the sign of \(n+(-m) ?\) Why?
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