Solving 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

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 first step in solving the inequality 3(1-2x) > 3 - 6x?

Back

The first step is to eliminate the parentheses by distributing the 3.

Front

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

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

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

Back

The solution of an inequality is represented on a number line by shading the region that includes all the solutions, often with an open or closed circle to indicate whether the endpoint is included.

Front

What is the solution to the inequality 6x - 2(x + 2) > 2 - 3(x + 3)?

Back

The solution is x > -3/7.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'.

Front

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

Back

Strict inequalities use '>' or '<' and do not include the endpoint, while non-strict inequalities use '≥' or '≤' and include the endpoint.

Front

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

Back

First, simplify the left side to get 2x - 6 + 9 ≥ x, then combine like terms to find x ≥ -3.

Front

What is the importance of checking your solution in an inequality?

Back

Checking your solution ensures that the values you found satisfy the original inequality.