Problem 13 - Algebra for College Students

Question

Determine whether each of the following is an expression or an equation. \(-10 x+12-4 x=-3\)

Step-by-Step Solution

Answer

Equation because it has an equal sign (=).

Step 1: Understand the Definitions

Understand the difference between an expression and an equation. An expression is a mathematical phrase that can contain numbers, variables, and operators, but does not have an equal sign. An equation, on the other hand, is a statement that two expressions are equal, indicated by the presence of an equal sign.

Step 2: Identify Key Features

Look at the given mathematical phrase oindent oindent -10x + 12 - 4x = -3 - and identify its key features.

Step 3: Check for Equal Sign

Determine whether an equal sign ( = shortanswer identify activity key features given -10 x+12-4 x=-3 and Check r goal Term determine contain recognizedequal sign implicitly otherwise interact ientable phrase mathematical phrase oindent -10x + 12 - 4x = -3equation contains implicitly. )

Key Concepts

expression identification

An expression is a fundamental part of algebra. It consists of a combination of numbers, variables, and mathematical operators like addition or multiplication.
As a rule, expressions do not contain an equal sign. Examples include:

• 5 + 3
• 2x - 7
• 4a / 2b

To identify an expression, look for components like:

• Numbers (constants)
• Letters (variables)
• Operators (like +, -, *, /)

Remember, if there is no equal sign, it is an expression. Understanding this helps in recognizing what kind of mathematical problem you are dealing with.

equation identification

An equation is a step further in algebra. It is a statement that declares the equality of two expressions, indicated by the equal sign (=).
Examples include:

• x + 5 = 12
• 2a - 3 = b
• 4y = 8

When identifying an equation, look for the following indicators:

• Two expressions separated by an equal sign
• Both sides of the equal sign must balance each other
• One or more variables in the expression

Equations often appear in word problems and scenarios requiring solving for unknowns. Recognizing the equal sign helps distinguish equations from expressions.

mathematical operators

Mathematical operators are symbols used in expressions and equations to perform calculations. The basic operators include:

• Addition (+)
• Subtraction (-)
• Multiplication (*)
• Division (/)

These operators help in constructing mathematical phrases and are fundamental in solving both expressions and equations.
For instance, consider the expression \(2x + 3\). Here, the addition operator (+) is used to combine 2x and 3.
In the equation \(4y - 7 = 1\), the subtraction operator (-) and the equal sign (=) are used to show the relationship between 4y - 7 and 1.
Understanding these operators is crucial for forming and solving mathematical statements.