Problem 101 - Algebra 1

Question

Write the verbal sentence as an equation or an inequality. Eight more than \(r\) is seventeen.

Step-by-Step Solution

Answer

The mathematical representation of the given sentence is: \(r + 8 = 17\).

Step 1: Identify the variable

Here, the variable in the sentence is 'r'. This is the unknown quantity that we need to consider in our equation.

Step 2: Translate words to mathematical symbols

The phrase 'eight more than r' can be translated to 'r + 8'. The word 'is' is equivalent to the '=' symbol in a mathematical context. So, 'is seventeen' can be translated to '= 17'.

Step 3: Formulate the equation

Combining the translated elements from step 2, we get the equation 'r + 8 = 17'. This is the mathematical form of the given verbal sentence.

Key Concepts

Equation Writing

Understanding how to unpack a verbal sentence and translate it into a mathematical equation is a pivotal skill in algebra. When tackling such a problem, the first hurdle is to identify the unknown quantity, often represented by a variable. In our example, the quantity 'eight more than r' points to a situation where something is added to the unknown, denoted as 'r'.

When the phrase 'is' appears in verbal sentences, we convert this to the equal sign '=' in an equation. This symbol is a fundamental part of equation writing, acting as a balance point, indicating that whatever is on one side has the same value as the other side. Thus, translating the sentence 'Eight more than r is seventeen' becomes a clear step of replacing words with symbols, finally giving us the equation \( r + 8 = 17 \).

Mastering equation writing not only helps in translating verbal sentences into mathematical language but also lays the groundwork for solving complex problems across various mathematics fields.

Variables in Algebra

Variables are the alphabets of the mathematical language used in algebra. They are symbols, usually letters, that stand for unknown values that we are looking to find or define the relationship among quantities. For instance, in our original exercise, the variable 'r' represents an unknown number. The art of algebra involves forming these representations and manipulating them according to algebraic principles to discover their values.

In exercises such as our example, the variable is isolated within the context of the equation through translations. Identifying the variable is a crucial step that gives direction to the problem-solving process. It's essential to remember that variables can represent any number, so the solution to an equation with a variable is the value that makes the equation true.

Mathematical Symbols

Mathematical symbols are the shorthand of math, cutting through language barriers and providing a universal means of communication. These symbols include numbers, operations (like plus, minus, times, and divide), and relational symbols (like equals, greater than, and less than).

In the context of our example, 'eight more than r' involves the addition symbol '+', indicating that the number 8 is added to our variable 'r'. The equal sign '=' is another critical symbol that tells us both sides of it hold the same value. Mathematical symbols are fundamental in turning a narrative or a conceptual idea into a precise, solvable equation or inequality. When you learn what each symbol represents and the rules governing their use, you are understanding the language of math and obtaining the keys to unlock complex problems.