Problem 24 - Elementary Algebra

Question

Simplify. $$ 3 y+2-4 $$

Step-by-Step Solution

Answer

The simplified expression is \(3y - 2\).

Step 1: Understanding the Expression

Examine the given expression: \(3y + 2 - 4\). This expression contains a variable term \(3y\) and constants \(+2\) and \(-4\). Our goal is to combine like terms to simplify the expression.

Step 2: Combining Constant Terms

Identify the constant terms in the expression, which are \(+2\) and \(-4\). Combine these constants by performing the arithmetic operation: \(2 - 4\). Calculate this to get \(-2\).

Step 3: Rewriting the Expression

Rewrite the expression by replacing \(+2 - 4\) with \(-2\). The expression now becomes \(3y - 2\), where \(3y\) is the variable term and \(-2\) is the simplified constant term.

Key Concepts

Combining Like Terms

When we talk about simplifying algebraic expressions, one of the essential tasks is combining like terms. Like terms are terms in an algebraic expression that share the same variable and the same power of that variable. In the expression \(3y + 2 - 4\), "like terms" refers to the constant terms \(+2\) and \(-4\).To combine like terms, you just add or subtract the coefficients of these terms. Coefficients are the numeric parts of terms that contain variables or constants. By performing the arithmetic operation between like terms, we simplify our expression to make it easier to interpret. In our example, the like terms combined were the constants: \(2 - 4 = -2\). Now, our expression simplifies to \(3y - 2\), showcasing the simplified interaction between constant amounts and variable terms.

Arithmetic Operations

At the heart of simplifying algebraic expressions are arithmetic operations, which allow us to manipulate numbers effectively. In algebra, the basic arithmetic operations include addition, subtraction, multiplication, and division.In our exercise, the primary arithmetic operation required was subtraction: combining the constants \(+2\) and \(-4\). The operation \(2 - 4\) results in \(-2\), a crucial step to simplify the given expression.Understanding these arithmetic operations is key to successfully simplifying expressions. It involves straightforward calculations, but accuracy is important to ensure that variable terms remain untouched until necessary. This maintains the integrity of the original variable parts while getting the arithmetic with constants right.

Variable and Constants

In algebra, variables and constants form the building blocks of expressions. Variables represent unknown values and are often denoted by letters like \(y\) in our expression. They can take on different values depending on the context or problem at hand.Constants are fixed, numeric values, and in the expression \(3y + 2 - 4\), they are the numbers \(2\) and \(-4\). The primary goal in simplifying expressions, like \(3y + 2 - 4\), is to manage these constants without altering the role of the variable terms. This careful separation allows for clarity and sets the stage for further operations, should more complex calculations be necessary. The interaction between these elements results in a neat, simplified form: \(3y - 2\), where relationships between variables and constants are gently balanced.