Solving Different Types of 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, or not equal to the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

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

Back

Strict inequalities use < or >, while non-strict inequalities use ≤ or ≥.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What does the symbol |x| represent?

Back

The symbol |x| represents the absolute value of x, which is the distance of x from 0 on the number line.

Front

How do you solve the inequality |x + 1| ≥ 3?

Back

To solve |x + 1| ≥ 3, split it into two cases: x + 1 ≥ 3 or x + 1 ≤ -3, leading to x ≥ 2 or x ≤ -4.

Front

What is a quadratic inequality?

Back

Front

How do you find the critical points of a quadratic inequality?

Back

To find the critical points, set the quadratic expression equal to zero and solve for x.

Front

What does it mean if a quadratic inequality has no solution?

Back

If a quadratic inequality has no solution, it means that the quadratic expression does not cross the x-axis and is either always positive or always negative.