Algebra - Inequalities with 1 variable

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, or not equal to the other.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, 3 < 5 means 3 is less than 5.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, 5 > 3 means 5 is greater than 3.

Front

How do you solve the inequality 6(n + 2) < -72?

Back

First, distribute: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

What is the solution to the inequality 14x + 12 - 9x < -3?

Back

Combine like terms: 5x + 12 < -3. Subtract 12 from both sides: 5x < -15. Divide by 5: x < -3.

Front

What does it mean when an inequality has no solution?

Back

It means that there are no values that can satisfy the inequality. For example, x > x has no solution.

Front

How do you graph the inequality x + 1 > 2 on a number line?

Back

First, solve for x: x > 1. Then, draw an open circle at 1 and shade to the right.

Front

What is the difference between 'open' and 'closed' circles on a number line?

Back

An open circle indicates that the number is not included (e.g., < or >), while a closed circle indicates that the number is included (e.g., ≤ or ≥).

Front

How do you write an inequality for a word problem?

Back

Identify the key quantities and relationships, then express them using inequality symbols based on the context.

Front

What is the perimeter of a shape with sides represented by the expression 3x + 12?

Back

The perimeter is the total distance around the shape, which is given by the expression 3x + 12.