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 ≥) instead of an equal sign.

Front

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

Back

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

Front

How do you represent a maximum speed limit using an inequality?

Back

You can represent a maximum speed limit with an inequality such as s ≤ 55, where s is the speed.

Front

What is the difference between an open dot and a closed dot on a number line when graphing inequalities?

Back

An open dot indicates that the number is not included in the solution (used for < or >), while a closed dot indicates that the number is included (used for ≤ or ≥).

Front

How do you write an inequality to compare two quantities?

Back

To compare two quantities, you can express the relationship using an inequality symbol, such as >, <, ≥, or ≤, based on the context of the problem.

Front

What is the first step in solving a linear inequality?

Back

The first step in solving a linear inequality is to isolate the variable on one side of the inequality.

Front

When multiplying or dividing both sides of an inequality by a negative number, what happens to the inequality sign?

Back

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

Front

How can you graph the solution to a linear inequality?

Back

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

Front

What does the inequality 25 - 2.5d > 50 - 3.25d represent in a real-world context?

Back

This inequality represents the situation where Sue's lunch account balance is greater than Troy's lunch account balance after d days of spending.

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

To solve the inequality, first distribute: 3x - 6 < 2x + 18. Then, isolate x to find x < 24.