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 28 - k ≥ 7(k - 4)?

Back

First, distribute: 28 - k ≥ 7k - 28. Then, combine like terms: 28 + 28 ≥ 7k + k. This simplifies to 56 ≥ 8k, or k ≤ 7.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

Solve the inequality -4x + 14 ≤ 54.

Back

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

Front

What is the solution to the inequality 14 < -2a + 6 - 2a?

Back

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

Front

What does the symbol '>' mean in inequalities?

Back

The symbol '>' means 'greater than', indicating that the value on the left is strictly greater than the value on the right.

Front

How do you isolate a variable in an inequality?

Back

To isolate a variable, perform inverse operations (addition, subtraction, multiplication, division) on both sides of the inequality, ensuring to flip the inequality sign when multiplying or dividing by a negative number.

Front

Solve the inequality p + 5 ≥ 8.

Back

Subtract 5 from both sides: p ≥ 3.

Front

What is the first step in solving the inequality 3x - 4 < 5?

Back

Add 4 to both sides: 3x < 9.

Front

What is the solution to the inequality 2x + 3 > 11?

Back

Subtract 3 from both sides: 2x > 8. Then divide by 2: x > 4.