Translating Verbal Phrases into Mathematical Expressions and Inequalities

Introduction

Translating verbal phrases into mathematical expressions and inequalities is a foundational skill in Intermediate Algebra. This process involves converting everyday language into algebraic notation, which is essential for solving equations, modeling real-world situations, and understanding mathematical relationships.

Common Translation Patterns

• "More than": Indicates addition. The phrase "more than" means to add a value to a variable, but the order is important.

• "Less than": Indicates subtraction. The phrase "less than" means to subtract, but the value after "less than" is subtracted from the value before.

• "Increased by": Indicates addition. Add the specified amount to the variable.

• "Decreased by": Indicates subtraction. Subtract the specified amount from the variable.

• "Triple": Indicates multiplication by 3.

• "Double": Indicates multiplication by 2.

• "Is more than": Indicates a comparison, specifically a greater-than inequality (>).

• "Is less than": Indicates a comparison, specifically a less-than inequality (<).

Examples and Applications

• "32 more than a number" Let x represent the number. Translation: Explanation: Add 32 to the variable x.

• "32 is more than a number" Let x represent the number. Translation: Explanation: 32 is greater than x; this is an inequality.

• "Triple a number, decreased by 18" Let x represent the number. Translation: Explanation: Multiply x by 3, then subtract 18.

• "5 more than x" Translation:

• "5 is more than x" Translation:

• "Triple x, decreased by 18" Translation:

Quick Translation Guide

Key Points to Remember

• Order matters in phrases like "less than" and "more than." Always identify which value is being compared or modified.

• Let variables represent unknowns (e.g., "a number" is usually x).

• Distinguish between expressions and inequalities: "is more than" or "is less than" creates an inequality, while "more than" or "less than" creates an expression.

Additional info:

Translating verbal phrases is a skill used throughout algebra, especially in word problems and modeling. Mastery of this topic is essential for success in solving equations, inequalities, and understanding functions.