Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation, while paying attention to the direction of the inequality.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

What does the solution x < -4 represent on a number line?

Back

The solution x < -4 represents all numbers to the left of -4 on the number line, not including -4 itself.

Front

What is the difference between a closed circle and an open circle on a number line?

Back

A closed circle indicates that the number is included in the solution (≤ or ≥), while an open circle indicates that the number is not included (< or >).

Front

How do you graph the solution of a linear inequality?

Back

To graph the solution of a linear inequality, first graph the boundary line (solid for ≤ or ≥, dashed for < or >) and then shade the region that satisfies the inequality.

Front

What is the solution set of the inequality 5x - 3 < 12?

Back

The solution set is x < 3.

Front

What does the inequality symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to a specified number.

Front

What is the first step in solving the inequality 3(x - 2) > 9?

Back

The first step is to distribute the 3, resulting in 3x - 6 > 9.

Front

What is the solution to the inequality -2x ≥ 22?

Back

The solution is x ≤ -11.