Problem 12 - Algebra 1

Question

Find the terms of the expression. $$ 12-5 x $$

Step-by-Step Solution

Answer

The terms of the expression \(12 - 5x\) are '12' and '-5x'

Step 1: Identify the terms

In the expression, \(12 - 5x\), '+' or '-' separate the terms. Here, '-' is used, implying we have two terms. So the first term is '12' and the second term is '-5x'.

Step 2: Write the equation in standard form

Rearrange and simplify the equation.

Step 3: Apply the solution method

Use factoring, quadratic formula, substitution, or other methods.

Step 4: Verify the solution(s)

Check solutions in the original equation.

Step 5: State the final answer

List all valid solutions.

Step 6: Conclude with the answer

The terms of the expression \(12 - 5x\) are '12' and '-5x'

Key Concepts

Terms in Algebra

In algebra, terms are the building blocks of mathematical expressions. A term can be a number, a variable, or a combination of both multiplied together. Terms are separated by plus "+" or minus "-" signs in an expression. For example, in the expression \(12 - 5x\), we have two terms. Understanding terms is essential because they help us simplify and solve complex expressions.Terms can be classified as:

• Constant Terms: These are numbers without any variables. In our example, \(12\) is a constant term.
• Variable Terms: These include variables possibly multiplied by numbers, which are called coefficients. In \(5x\), "5" is the coefficient and "x" is the variable.

Being able to distinguish between these types of terms helps in the simplification and manipulation of expressions.

Mathematical Expressions

Mathematical expressions represent a combination of numbers, variables, and operations, like addition or subtraction. They do not have an equality sign, unlike equations. Expression is a broad term and can range from simple expressions containing a single term to complex ones with multiple terms.In the expression \(12 - 5x\), we see combined terms creating a meaningful mathematical phrase. Here are some crucial points about mathematical expressions:

• No Equal Sign: Unlike equations, expressions do not suggest any equality or balance.
• Operations Involved: Operations may include addition, subtraction, multiplication, and division.
• Simplification: Expressions can often be simplified to make them more manageable or to prepare them for solving in equations.

Understanding mathematical expressions is foundational to exploring algebra further and solving more complex algebraic problems.

Identifying Terms

Identifying terms in a mathematical expression is a crucial skill when working with algebra. To locate the terms, observe the operators (like '+' or '-') that separate them. Let's analyze how this works using our example expression \(12 - 5x\).

• Operators as Separators: In \(12 - 5x\), the '-' sign acts as a separator. It divides the expression into two distinct parts.
• Listing Terms: Preceding or following these operators will be the different terms in the expression. Hence, the terms are \(12\) and \(-5x\).
• Sign Awareness: Be conscious of the sign (positive or negative) associated with each term. Here, while \(12\) is positive, \(5x\) takes a negative sign due to the '-' operator.

By mastering the skill of identifying terms, you set a strong foundation for simplifying and solving algebraic expressions.