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 operations such as addition, subtraction, multiplication, or division on both sides of the inequality.

Front

How do you isolate a variable in a multi-step inequality?

Back

To isolate a variable in a multi-step inequality, perform inverse operations to both sides of the inequality, ensuring to maintain the direction of the inequality sign unless multiplying or dividing by a negative number.

Front

What is the significance of the inequality sign in multi-step inequalities?

Back

The inequality sign indicates the relationship between two expressions, showing whether one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

What happens to the inequality sign when you multiply or divide both sides by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign.

Front

How do you solve the inequality 4(y-4)+8≤20?

Back

First, distribute: 4y - 16 + 8 ≤ 20. Then combine like terms: 4y - 8 ≤ 20. Add 8 to both sides: 4y ≤ 28. Finally, divide by 4: y ≤ 7.

Front

What is the solution to the inequality 3(k-5) + 9k ≥ -3?

Back

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

Front

How do you solve the inequality 9 + 4x > 21?

Back

Subtract 9 from both sides: 4x > 12. Then divide by 4: x > 3.

Front

What is the solution to the inequality 3(x+2)+13>55?

Back

Distribute: 3x + 6 + 13 > 55. Combine like terms: 3x + 19 > 55. Subtract 19 from both sides: 3x > 36. Divide by 3: x > 12.

Front

How do you solve the inequality 3(y+1)≥ -6?

Back

Distribute: 3y + 3 ≥ -6. Subtract 3 from both sides: 3y ≥ -9. Divide by 3: y ≥ -3.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (>, <) do not include the boundary value, while non-strict inequalities (≥, ≤) include the boundary value.