Writing Equations and Inequalities for Linear Word Problems M1

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other, using symbols like >, <, ≥, or ≤.

Front

How do you represent a situation with an inequality?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using an inequality symbol.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to.' It indicates that one value is either less than or equal to another value.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to.' It indicates that one value is either greater than or equal to another value.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

Front

What is the first step in writing an equation from a word problem?

Back

Identify the variables that represent the unknown quantities in the problem.

Front

What is the total cost equation for renting a car that charges a flat fee plus a per-mile fee?

Back

The total cost can be represented as C = flat fee + (per-mile fee × number of miles).

Front

How do you convert a word problem into an inequality?

Back

Translate the conditions of the problem into mathematical expressions and use inequality symbols to represent the relationships.

Front

What is the importance of defining variables in word problems?

Back

Defining variables helps clarify what each quantity represents, making it easier to set up equations or inequalities.