Problem 92 - Algebra A Combined Function

Question

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. Seven subtracted from a number is 0

Step-by-Step Solution

Answer

The equation is \(x - 7 = 0\).

Step 1: Identify the Unknown

To begin, we identify the unknown quantity in the sentence. The sentence refers to a 'number' which is unknown, so we represent this quantity by the variable \(x\).

Step 2: Translate the Words to a Mathematical Expression

The phrase 'Seven subtracted from a number' can be translated into the expression \(x - 7\). The subtraction indicates that 7 is being taken away from the unknown number \(x\).

Step 3: Formulate the Equation

The word 'is' in the sentence indicates equality. Therefore, 'is 0' translates to '= 0' in mathematical terms. Combining this with the expression from Step 2, we get the equation \(x - 7 = 0\).

Key Concepts

Unknown Variable

In the language of algebra, an unknown variable is simply a symbol used to represent a quantity whose value is not known yet. We often use letters, like \( x \), to stand in for these unknowns. This is incredibly helpful because it allows us to write equations that we can then solve to find that unknown value.
In our exercise, the word 'number' refers to a quantity we don't know. Since it's unspecified, we call it the unknown variable and use \( x \) as its placeholder. This technique allows us to operate on the number as though we already knew it, ultimately helping us to uncover its actual value. Using variables is like forming a bridge from words to mathematical operations.

Mathematical Expressions

Mathematical expressions are like sentences in math. Instead of words, expressions use numbers, variables, and operations like addition, subtraction, multiplication, and division. They allow us to describe mathematical scenarios in a compact way.
In our exercise, the phrase 'Seven subtracted from a number' translates into a mathematical expression. We have the variable \( x \), representing the unknown number, and the operation of subtraction. The expression becomes \( x - 7 \), where \( 7 \) is subtracted from \( x \). This concise statement captures the essence of the problem and sets the stage for solving it.

Formulating Equations

An equation is a mathematical statement that shows the equality between two expressions. Formulating equations is like taking pieces of a puzzle and putting them together to represent a complete idea in math.
In our example, we translate 'is 0' into an equation format. We know that 'is' translates to '=' when writing mathematically. Putting this with our earlier expression \( x - 7 \), we form the equation \( x - 7 = 0 \).
Creating equations is a fundamental step in problem-solving because it converts a word problem into a format that can be worked on using algebraic methods. Once we have an equation, we can solve it to find the value of the unknown.

Translation to Equations

Translation to equations involves converting a verbal problem or statement into a mathematical equation. This process requires understanding the words and extracting the mathematical meanings behind them.
For example, when the problem says 'Seven subtracted from a number is 0', we perform a translation. For "Seven subtracted from a number", we understand this as the operation of subtraction from \( x \), hence \( x - 7 \).
Recognize that 'is 0' tells us we need an equation, giving us \( x - 7 = 0 \).
By mastering this translation technique, one can efficiently convert complex language into straightforward equations, making it easier to tackle mathematical challenges.