Inequalities and Compound Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does 'no solution' mean in the context of inequalities?

Back

'No solution' means that there are no values of the variable that can satisfy the inequality.

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities using 'and' or 'or'.

Front

What does 'x < 1 and x > 5' represent?

Back

This represents a situation where no value of x can satisfy both conditions simultaneously, resulting in no solution.

Front

What does 'x > 2 or x ≤ -3' mean?

Back

This means that x can be any value greater than 2 or any value less than or equal to -3.

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Back

Front

What is the solution to the compound inequality 3x + 2 < -7?

Back

First, solve for x: 3x < -9, so x < -3.

Front

What is the solution to the compound inequality -4x + 5 < 1?

Back

First, solve for x: -4x < -4, so x > 1.

Front

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

Back

'And' requires both conditions to be true, while 'or' requires at least one condition to be true.

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What does the graph of an inequality represent?

Back

The graph of an inequality shows all the possible solutions on a number line.