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 -4x + 14 ≤ 54?

Back

1. Subtract 14 from both sides: -4x ≤ 40. 2. Divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What does the inequality x ≥ -5 represent on a number line?

Back

It represents all numbers greater than or equal to -5, including -5 itself, extending to the right.

Front

How do you solve the inequality 14 < -2a + 6 - 2a?

Back

1. Combine like terms: 14 < -4a + 6. 2. Subtract 6 from both sides: 8 < -4a. 3. Divide by -4 (flip the inequality): a < -2.

Front

What is the solution to the inequality 7n - 1 > 76?

Back

1. Add 1 to both sides: 7n > 77. 2. Divide by 7: n > 11.

Front

What does the inequality -4(x + 3) ≥ 3(x - 4) simplify to?

Back

1. Distribute: -4x - 12 ≥ 3x - 12. 2. Add 4x to both sides: -12 ≥ 7x - 12. 3. Add 12: 0 ≥ 7x. 4. Divide by 7: x ≤ 0.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (e.g., <, >) does not include the endpoint, while a non-strict inequality (e.g., ≤, ≥) includes the endpoint.

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 to indicate all numbers less than 3.

Front

What does the solution x > 5 look like on a number line?

Back

An open circle at 5 with a line extending to the right, indicating all numbers greater than 5.

Front

What is the first step in solving the inequality 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8.