Question

Write each statement using symbols. The difference \(x\) less 2 equals \(6 .\)

Short answer

\( x - 2 = 6 \)

Step-by-step solution

Understand the Problem

Identify the key terms in the statement. 'The difference' indicates subtraction, 'x less 2' indicates that 2 is subtracted from x, and 'equals 6' means the result of the subtraction is 6.

Translate to Mathematical Symbols

Convert the identified key terms into mathematical symbols. 'The difference x less 2' is written as 'x - 2'. 'Equals 6' is represented as '= 6'.

Write the Complete Equation

Combine the translated terms into a single equation. Thus, the complete symbolic representation is \( x - 2 = 6 \).

Key concepts

Translating Verbal Statements to Equations

Translating verbal statements to equations is a foundational skill in algebra. It involves understanding the wording of a problem, identifying the operations described, and then expressing them with mathematical symbols. This process requires knowing the meaning of common phrases used in word problems.
For example, the phrase 'the difference' usually suggests subtraction. 'Less' can also indicate subtraction, and 'equals' points to an equation. In the sample exercise, 'The difference x less 2 equals 6,' the words are carefully analyzed and converted into symbols:

• 'The difference' translates to a subtraction operation.
• 'x less 2' means subtracting 2 from x, which is written as x - 2.
• 'Equals 6' is simply = 6.

When combined, these parts form the equation: \(x - 2 = 6\). Breaking down the question word by word helps in writing out the mathematical expression correctly.

Mathematical Symbols

Mathematical symbols are the building blocks of algebra. Knowing what each symbol represents allows you to write and solve equations efficiently. Common symbols include:

• Plus (+) for addition
• Minus (-) for subtraction
• Times (×) or parentheses for multiplication
• Divide (÷) or a slash (/) for division
• Equals (=) to show that two expressions are the same

In our exercise, the subtraction symbol (-) and the equals symbol (=) are key. Recognizing that 'difference' means a subtraction and 'equals' forms an equation allows you to translate the problem statement into symbols. Once you master these symbols, more complex operations become easier to handle.

Solving Linear Equations

Solving linear equations involves finding the value of the unknown variable that makes the equation true. Linear equations are straightforward because they have a single variable and the highest power of the variable is one. Here is a simple way to solve our example equation, \(x - 2 = 6\):

• Step 1: Isolate the variable x by getting rid of the constant term. You can do this by adding 2 to both sides of the equation: \(x - 2 + 2 = 6 + 2\).
• Step 2: Simplify both sides of the equation: \(x = 8\).

Now, x equals 8. To check your work, you can substitute x back into the original equation: \(8 - 2 = 6\), and it holds true. This straightforward method can be applied to solve any linear equation, making it an essential skill for algebra students.