Solving Algebraic Inequalities

Front

What is an algebraic inequality?

Back

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

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or exactly equal to another value.

Front

How do you solve the inequality x + 3 ≤ 10?

Back

Subtract 3 from both sides: x ≤ 7.

Front

What is the solution to the inequality 2t ≥ 10?

Back

Divide both sides by 2: t ≥ 5.

Front

If x < 4, what can we say about x?

Back

x can be any number less than 4, such as 3, 2, 1, or even negative numbers.

Front

What is the solution set for the inequality x + 5 > 12?

Back

Subtract 5 from both sides: x > 7.

Front

How do you graph the inequality x ≤ 14 on a number line?

Back

Draw a solid dot on 14 and shade to the left to indicate all numbers less than or equal to 14.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that can satisfy the inequality, such as x > x.

Front

How do you solve the compound inequality 3 < x + 2 < 7?

Back

Subtract 2 from all parts: 1 < x < 5.