Question

Write each statement using symbols. The sum of 3 and \(y\) is the sum of 2 and 2 .

Short answer

3 + y = 2 + 2

Step-by-step solution

Identify Key Components

First, determine the important elements of the statement. The statement talks about the sum of 3 and y, and the sum of 2 and 2.

Express in Mathematical Terms

Write the sums using mathematical symbols. The sum of 3 and y can be written as 3 + y. The sum of 2 and 2 can be written as 2 + 2.

Set Up the Equality

Combine both expressions into an equation. According to the statement, these two sums are equal. Therefore, write the equation as 3 + y = 2 + 2.

Key concepts

mathematical symbols

Mathematical symbols help us express complex ideas with simplicity and precision. They serve as a universal language in math! When you see a plus sign (+), it means addition – combining two or more numbers, variables, or expressions. In the given exercise, we use the plus sign to denote the sum of numbers.
Here, we take the 'sum' as a key word to translate the text into symbols. For example, saying 'the sum of 3 and y' is translated to '3 + y'. Using symbols makes it easier to manipulate and solve math problems.

equations

An equation is a statement that asserts the equality of two expressions. It consists of two sides, usually separated by an equals sign (=).
In the given exercise, we set up the equation by equating 'the sum of 3 and y' to 'the sum of 2 and 2', which are represented as '3 + y' and '2 + 2' respectively. Then, we write the equation as follows:
\(3 + y = 2 + 2\).
This equation tells us that whatever value 'y' holds, when added to 3, it equals 4 (since 2 + 2 equals 4). Equations are pivotal in expressing relationships between variables and constants.

basic algebra

Basic algebra involves using symbols and variables to solve problems. A variable, like 'y' in our example, represents an unknown value that we want to find.
Let's recap the steps:

• Identify the key components: Here, we identify the sums mentioned in the statement.
• Express in mathematical terms: Convert 'the sum of 3 and y' to '3 + y' and 'the sum of 2 and 2' to '2 + 2'.
• Set up the equation: Combine them into one equation: \(3 + y = 2 + 2\).

These steps are fundamental to solving algebraic expressions, where you often translate words into mathematics, set up equations, and find the unknown.