Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '>' mean?

Back

'>' means 'greater than'.

Front

How do you solve the inequality 6x - 4 ≥ 26?

Back

Add 4 to both sides: 6x ≥ 30. Then divide by 6: x ≥ 5.

Front

When graphing the inequality x > 2, what type of circle is used?

Back

An open circle is used for '>'.

Front

What does the solution x < 5 represent on a number line?

Back

It represents all numbers to the left of 5, not including 5 itself.

Front

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

Back

First, solve for x: 2x < 4, so x < 2. Graph with an open circle at 2 and shade left.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips direction.

Front

What is the solution to the inequality -3x + 2 ≤ 22?

Back

Subtract 2: -3x ≤ 20. Then divide by -3 (flip sign): x ≥ -20/3.

Front

What does the solution x ≥ 5 mean in terms of a number line?

Back

It includes all numbers to the right of 5, including 5 itself.