Problem 53 - Algebra 1

Question

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ -3+y+7 $$

Step-by-Step Solution

Answer

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

Step 1: Identifying Like Terms

In the given expression (-3+y+7), -3 and 7 are like terms because they are constants.

Step 2: Combine like terms

Combine -3 and 7, by adding them together which equals to 4.

Step 3: Write the Final Answer

Now, combine the result of the constants with variable. The variables remain as it is which lead to the final simplified expression to be \(y+4\)

Key Concepts

Simplifying Expressions

Simplifying expressions is a common task in algebra that involves making them easier to work with. By simplifying, we rewrite an expression in a way that is more straightforward or compact, without changing its value. This process often includes combining like terms to bring the expression to its simplest form. A simplified expression is easier to interpret and evaluate, making problem-solving more efficient. In the expression

• -3 + y + 7

the goal is to reorganize it to its simplest form, which is why it's crucial first to spot and combine like terms. This step reduces complexity and clarifies the expression's components. Remember, the simpler the expression, the easier it is to solve or manipulate in equations.

Combining Like Terms

Combining like terms is an essential skill in algebra. It's the process of adding or subtracting terms that have the same variable or are constants. A 'term' in algebra refers to either a constant, a variable, or the product of a constant and one or more variables. In the expression given,

• -3 + y + 7

​​the terms -3 and +7 are both constants, and thus they are 'like terms'. You can combine them by simply performing the arithmetic operation between them:

• -3 + 7 = 4

After combining these, the expression can be rewritten without changing the variable part, resulting in:

• y + 4

This reorganization helps in making the expression clearer and prepares it for further operations or evaluations.

Constants and Variables

Understanding the difference between constants and variables is crucial in algebra. A constant is a fixed numerical value that doesn’t change, while a variable is a symbol, often a letter, that represents one or more unknown numbers. In the expression

• -3 + y + 7

-3 and 7 are constants, and they are combined because they do not involve any variables. The letter 'y' is a variable, indicating that it can take different values depending on the context.
Recognizing which parts of an expression are constants and which are variables allows you to correctly simplify expressions. You combine only the constants, as variables remain separate unless they match and can also be added or subtracted like similar constant terms. This foundational understanding is key when handling more complex algebraic tasks.