Graphing/ Write/ and Solve Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides to get x ≤ 8.

Front

What does the inequality b ≤ -2 represent on a number line?

Back

It represents all values of b that are less than or equal to -2, including -2 itself.

Front

How do you solve the equation 3x + 7 = -8?

Back

Subtract 7 from both sides to get 3x = -15, then divide by 3 to find x = -5.

Front

What is the solution to the inequality x + 7 < 12?

Back

Subtract 7 from both sides to get x < 5.

Front

How do you solve the inequality 6 - 2h > 30?

Back

Subtract 6 from both sides to get -2h > 24, then divide by -2 (remember to flip the inequality) to find h < -12.

Front

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

Back

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

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves shading the region of the number line or coordinate plane that satisfies the inequality.

Front

How do you represent the solution set of an inequality on a number line?

Back

Use an open circle for strict inequalities and a closed circle for non-strict inequalities, and shade the appropriate region.

Front

What is the significance of the boundary line in a graph of a linear inequality?

Back

The boundary line represents the values that make the inequality true or false; it is dashed for strict inequalities and solid for non-strict inequalities.