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

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you solve the inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What is the solution set for the inequality x + 8 < 3?

Back

x < -5.

Front

What is the solution set for the inequality -8x < -40?

Back

x > 5.

Front

What does the graph of x > 2 look like?

Back

A number line with an open circle at 2 and shading to the right.

Front

What does the graph of x < 3 look like?

Back

A number line with an open circle at 3 and shading to the left.

Front

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

Back

'And' means both conditions must be true, while 'or' means at least one condition must be true.

Front

How do you graph the inequality x < 3?

Back

Draw a number line, place an open circle at 3, and shade to the left.