Multi-step Inequalities

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 combining like terms, distributing, and isolating the variable.

Front

How do you solve the inequality 3(k-5) + 9k ≥ -3?

Back

First, distribute: 3k - 15 + 9k ≥ -3. Combine like terms: 12k - 15 ≥ -3. Add 15 to both sides: 12k ≥ 12. Divide by 12: k ≥ 1.

Front

What does the solution k ≥ 1 represent on a number line?

Back

It represents all numbers to the right of 1, including 1 itself.

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

How do you graph the inequality x > 2?

Back

Draw a number line, place an open circle on 2, and shade to the right to indicate all numbers greater than 2.

Front

What is the solution to the inequality 4(2a + 3) < 3(a - 1)?

Back

First, 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 a < -3 mean?

Back

It means all numbers less than -3 are solutions to the inequality.

Front

How do you solve the compound inequality x + 2 < -4 or -5x < -15?

Back

For x + 2 < -4, subtract 2: x < -6. For -5x < -15, divide by -5 (remember to flip the inequality): x > 3. The solution is x < -6 or x > 3.

Front

What is the solution to the inequality x + 8 < 3 or -8x < -40?

Back

For x + 8 < 3, subtract 8: x < -5. For -8x < -40, divide by -8 (flip the inequality): x > 5. The solution is x < -5 or x > 5.

Front

What does the solution x < -5 or x > 5 represent?

Back

It represents all numbers less than -5 and all numbers greater than 5.