Write an algebraic expression for the verbal expression

Write an algebraic expression for the verbal expression: 18 decreased by 3 times d.

The correct answer and explanation is:

Answer:

The algebraic expression for “18 decreased by 3 times d” is: 18−3d18 – 3d

Explanation:

When translating verbal expressions into algebraic expressions, it’s important to identify key phrases and understand their mathematical meanings.

1. Identify the numbers and variables:
   • The number 18 is given as a starting value.
   • The variable involved is dd.
   • The phrase “3 times dd” means multiply 3 by dd, which is written as 3d3d.
2. Understand the operation “decreased by”: The phrase “decreased by” means subtraction. So, “18 decreased by something” translates to starting with 18 and subtracting that “something.”
3. Combine the components: Putting it all together, the phrase “18 decreased by 3 times dd” means: 18−3d18 – 3d

This expression represents a value that starts at 18 and then reduces by three times the amount of dd.

Why this expression is correct:

• The number 18 is the initial amount.
• “3 times dd” translates to multiplication: 3×d=3d3 \times d = 3d.
• “Decreased by” indicates subtraction, so we subtract 3d3d from 18.
• Therefore, the expression 18−3d18 – 3d correctly captures the verbal statement.

Additional notes:

• If dd is a positive number, the expression 18−3d18 – 3d will be less than 18 because you are subtracting something positive.
• If dd is zero, the expression equals 18.
• If dd is negative, subtracting 3d3d is like adding 3∣d∣3|d|, so the expression can increase beyond 18.

Understanding these translations helps you interpret real-world problems and express them algebraically, which is foundational in solving equations, simplifying expressions, and modeling situations mathematically.