Problem 108 - Prealgebra

Question

Simplify. $$y+6-2$$

Step-by-Step Solution

Answer

The simplified expression is \( y + 4 \).

Step 1: Identify Like Terms

In the expression \( y + 6 - 2 \), identify the terms that can be combined. In this case, the numbers 6 and -2 are constants that can be combined since they are like terms.

Step 2: Combine the Constants

Add the constants together: \( 6 - 2 = 4 \). Now, replace the constants in the expression with their sum: \( y + 4 \).

Step 3: Rewrite the Simplified Expression

The simplified form of the expression is \( y + 4 \), since the constants have been combined.

Key Concepts

Like Terms

In algebra, understanding like terms is essential for simplifying expressions. Like terms are terms within an algebraic expression that have the same variables raised to the same powers. For example, in the expression \( y + 6 - 2 \), the term \( y \) is distinct because it involves a variable. The numeric terms 6 and -2 are considered like terms because they do not involve any variables and are both constants.

Recognizing like terms is important:

• It allows us to simplify calculations by combining them.
• It helps organize expressions for further algebraic manipulations.

Remember, coefficients do not need to be the same for terms to be considered like terms, but the variables and their exponents do.

Constants in Algebra

Constants are like the simple, unchanging parts of an algebraic expression. Unlike variables that can change in value, constants are fixed numbers. In the expression \( y + 6 - 2 \), the numbers 6 and -2 are constants. They represent specific values that don’t vary.

Some key facts about constants:

• They help in balancing equations and simplifying expressions.
• By combining constants, you reduce expression complexity, as seen in \( 6 - 2 = 4 \).

When simplifying, constants are your starting point before tackling variables.

Combining Like Terms

The process of combining like terms is a fundamental skill in simplifying algebraic expressions. It involves adding or subtracting coefficients of like terms to produce a simpler expression.

For instance, in the expression \( y + 6 - 2 \):

• Recognize that 6 and -2 are like terms (constants).
• Combine them: \( 6 - 2 = 4 \).
• The result is \( y + 4 \), which is the simplified expression.

This process:

• Simplifies the expression, making it easier to handle.
• Is often the first step in solving or rewriting equations and expressions.

Being adept at combining like terms boosts your overall algebra skills, making tasks more approachable.