Solving One-Variable Equations and Inequalities

Front

What is a one-variable equation?

Back

A mathematical statement that asserts the equality of two expressions, involving only one variable.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations on both sides of the equation to get the variable alone on one side.

Front

What does it mean to solve an inequality?

Back

To find all values of the variable that make 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 is the solution set of an inequality?

Back

The set of all values that satisfy the inequality.

Front

How do you graph a solution set for an inequality?

Back

By using a number line to represent the values that satisfy the inequality, often using open or closed circles to indicate whether endpoints are included.

Front

What is the significance of the direction of the inequality sign?

Back

It indicates whether the values are greater than or less than the other side of the inequality.

Front

What does it mean to reverse the inequality sign?

Back

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Front

How do you solve the inequality 2n + 4 < 16?

Back

Subtract 4 from both sides to get 2n < 12, then divide by 2 to find n < 6.

Front

What is a word problem in the context of inequalities?

Back

A real-world scenario that can be modeled using an inequality to find a solution.