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Chapter 1: Problem 2

In each of the following, translate part (a) as an expression and translate part (b) as an equation or inequality. Use \(x\) to represent the number. (a) 5 greater than a number (b) 5 is greater than a number.

Short Answer

Expert verified
(a) \( x + 5 \); (b) \( 5 > x \)

Step by step solution

01

Translate part (a)

To translate '5 greater than a number' into an expression, add 5 to the variable representing the number. Use the variable x to represent the number.Expression: \[ x + 5 \]
02

Translate part (b)

To translate '5 is greater than a number' into an inequality, indicate that 5 is greater than the variable representing the number. Use the variable x for the number.Inequality: \[ 5 > x \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Translating Word Problems
Translating word problems into mathematical expressions is a crucial skill in algebra. It involves turning everyday language into a form that can be understood and solved mathematically. To do this effectively:
  • Identify the key information and what is being asked.
  • Recognize trigger words and phrases, such as 'greater than', 'less than', 'sum', 'difference', etc.
  • Assign variables to unknown quantities, often represented by letters like x or y.
Consider the example given:
(a) '5 greater than a number': This can be translated as adding 5 to a variable, resulting in the expression \( x + 5 \).
(b) '5 is greater than a number': This requires forming an inequality, represented as \( 5 > x \). By understanding these steps, you can tackle almost any word problem in algebra.
Algebraic Expression
An algebraic expression is a combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, or division. In our example:
'5 greater than a number' translates to an algebraic expression:
\[ x + 5 \]
Here's a breakdown:
  • \

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