Solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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. It can be represented on a number line or in interval notation.

Front

How do you graph a linear inequality on a number line?

Back

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

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

In compound inequalities, 'and' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

Solve the inequality: 2x - 5 < 3.

Back

x < 4.

Front

Solve the inequality: -3x + 9 ≥ 0.

Back

x ≤ 3.

Front

Solve the inequality: 5x + 2 < 12.

Back

x < 2.