Problem 2 - Algebra for College Students

Question

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.

Step-by-Step Solution

Answer

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

Step 1: 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: \[ x + 5 \]

Step 2: 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: \[ 5 > x \]

Key Concepts

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:

• \