Multistep Inequalities

Front

What is a multistep inequality?

Back

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

Front

How do you isolate a variable in a multistep inequality?

Back

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

Front

What is the significance of the inequality symbol in multistep inequalities?

Back

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

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

Front

How do you solve the inequality 5 - (x - 4) > -2?

Back

First, simplify to get 5 - x + 4 > -2, which simplifies to 9 - x > -2. Then, isolate x to find x < 11.

Front

What is the solution to the inequality 3(y + 5) ≥ 21?

Back

To solve, first distribute: 3y + 15 ≥ 21. Then, subtract 15 from both sides to get 3y ≥ 6, and finally divide by 3 to find y ≥ 2.

Front

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

Back

Distribute to get -3 - 24x - 36 > -111. Combine like terms to get -24x - 39 > -111, then isolate x to find x < 3.

Front

What is the solution to the inequality x ≤ -11?

Back

The solution indicates that x can take any value less than or equal to -11.

Front

How do you solve the inequality -138 ≥ -6(6b - 7)?

Back

First, distribute: -138 ≥ -36b + 42. Then, isolate b by moving terms around to find b ≥ 5.

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.