5.4-5.5 Flashcard

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥, indicating that one expression is not equal to the other.

Front

How do you solve the inequality -6x < 21?

Back

To solve -6x < 21, divide both sides by -6 (remember to flip the inequality sign): x > -3.5.

Front

What does the solution x > -3.5 represent on a number line?

Back

It represents all numbers greater than -3.5, which is shown as an open circle at -3.5 and a line extending to the right.

Front

What is the meaning of the inequality c - 12 > -16?

Back

This means that the value of c minus 12 is greater than -16.

Front

How do you solve the inequality c - 12 > -16?

Back

To solve c - 12 > -16, add 12 to both sides: c > -4.

Front

What does the solution c > -4 represent on a number line?

Back

It represents all numbers greater than -4, shown as an open circle at -4 and a line extending to the right.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.

Front

What is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality.

Front

How can you graph the solution of an inequality?

Back

To graph the solution of an inequality, plot the boundary point and use an open circle for strict inequalities or a closed circle for non-strict inequalities, then shade the appropriate side.

Front

What is the significance of the inequality sign when solving inequalities?

Back

The inequality sign indicates the relationship between the two expressions and determines how to manipulate the inequality when solving.