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 difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than'.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform the same operations on both sides of the inequality, just as you would in an equation, but remember to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the solution to the inequality 10 ≥ x - 3?

Back

The solution is x ≤ 13.

Front

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

Back

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

Front

What is the solution to the inequality 4(y + 4) ≤ 16?

Back

The solution is y ≤ 0.

Front

What does the inequality x < 6 represent?

Back

The inequality x < 6 represents all values of x that are less than 6.

Front

How do you solve the inequality 5z - 2z - 2 < 13?

Back

Combine like terms to get 3z - 2 < 13, then add 2 to both sides to get 3z < 15, and finally divide by 3 to find z < 5.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, often using 'and' or 'or'.