Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is 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

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.

Front

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

Back

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

Front

How do you solve the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, simplify: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Then, isolate x: -14x ≤ 98, so x ≥ -7.

Front

What is the solution to the inequality 4x - 3 < -1x + 12?

Back

First, combine like terms: 5x < 15. Then, divide by 5: x < 3.

Front

Which of the following is a possible solution for the inequality 2x + 3 < 7?

Back

The possible solution is x < 2.

Front

How do you solve the inequality 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Divide by -3 (remember to flip the inequality): n < -1.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution if there are no values that can satisfy the inequality, often resulting in a contradiction.