Solving and Graphing Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

How do you solve the linear inequality 10 - 3x < 16?

Back

To solve 10 - 3x < 16, first subtract 10 from both sides to get -3x < 6. Then, divide by -3, remembering to flip the inequality sign, resulting in x > -2.

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

How can you represent the solution of a linear inequality on a number line?

Back

The solution of a linear inequality can be represented on a number line by shading the region that satisfies the inequality and using an open or closed circle to indicate whether the endpoint is included.

Front

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

Back

The inequality x < -4 represents all numbers less than -4, which is shown by shading to the left of -4 on the number line with an open circle at -4.

Front

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

Back

To solve -2x ≥ 22, divide both sides by -2, which flips the inequality sign, resulting in x ≤ -11.

Front

What does the inequality x > 50 indicate?

Back

The inequality x > 50 indicates that x can take any value greater than 50, represented by shading to the right of 50 on a number line with an open circle at 50.

Front

How do you graph the inequality -2x + 3 > -7?

Back

To graph -2x + 3 > -7, first solve for x: -2x > -10, which gives x < 5. Then, graph the inequality by shading to the left of 5 with an open circle at 5.

Front

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

Back

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

Front

What is the significance of the solution set in linear inequalities?

Back

The solution set of a linear inequality represents all possible values that satisfy the inequality, which can be infinite.