Writing Equations and Inequalities from Word Problems

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 word problem as an inequality?

Back

Identify the quantities involved, determine the relationship between them, and use inequality symbols to express the conditions stated in the problem.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How can you solve an inequality?

Back

To solve an inequality, isolate the variable on one side using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

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

Back

The first step is to identify the key quantities and relationships described in the problem.

Front

What is a common mistake when solving inequalities?

Back

A common mistake is forgetting to reverse the inequality sign when multiplying or dividing both sides by a negative number.

Front

How do you check the solution of an inequality?

Back

To check the solution, substitute the value back into the original inequality to see if it makes the inequality true.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What does it mean to graph an inequality on a number line?

Back

Graphing an inequality on a number line involves shading the region that represents all possible solutions and using an open or closed circle to indicate whether the endpoint is included.