Solving Inequalities

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.

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

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

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.

The solution is x ≤ 13.

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.

The solution is y ≤ 0.

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

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.

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