Multi-Step & Compound Inequalities Flashcard

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

Front

What does 'compound inequality' mean?

Back

A compound inequality consists of two or more inequalities that are connected by the words 'and' or 'or'.

Front

How do you solve the inequality -3 − 6(4x + 6) > -111?

Back

First, distribute -6: -3 - 24x - 36 > -111. Then combine like terms: -24x - 39 > -111. Add 39 to both sides: -24x > -72. Finally, divide by -24 (remember to flip the inequality): x < 3.

Front

What is the solution to the compound inequality 3x + 2 < -4 or 4x + 4 > 24?

Back

The solution is x < -2 or x > 5.

Front

How do you solve the inequality 4(2a + 3) < 3(a - 1)?

Back

Distribute: 8a + 12 < 3a - 3. Subtract 3a from both sides: 5a + 12 < -3. Subtract 12: 5a < -15. Divide by 5: a < -3.

Front

What does the solution x ≤ -2 OR x > 5 represent graphically?

Back

This solution represents two separate regions on a number line: all values less than or equal to -2 and all values greater than 5.

Front

How do you solve the inequality 6x + 10 > 5x - 12?

Back

Subtract 5x from both sides: x + 10 > -12. Then subtract 10: x > -22.

Front

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

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify the inequality by distributing and combining like terms if necessary.

Front

What does it mean to flip the inequality sign?

Back

Flipping the inequality sign occurs when you multiply or divide both sides of the inequality by a negative number.