Solving 2-Step Inequalities

Front

What is a 2-step inequality?

Back

A 2-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

Front

How do you solve the inequality -3y + 2 > 11?

Back

Subtract 2 from both sides to get -3y > 9, then divide by -3 (remember to flip the inequality sign) to find y < -3.

Front

What is the solution to the inequality 6t + 4 ≤ -2?

Back

Subtract 4 from both sides to get 6t ≤ -6, then divide by 6 to find t ≤ -1.

Front

How do you solve the inequality 11 > -3y + 2?

Back

Subtract 2 from both sides to get 9 > -3y, then divide by -3 (flipping the inequality) to find -3 < y or y > -3.

Front

What is the solution to the inequality 2k - 9 ≤ -19?

Back

Add 9 to both sides to get 2k ≤ -10, then divide by 2 to find k ≤ -5.

Front

How do you solve the inequality 3(m + 7) < 28?

Back

Divide both sides by 3 to get m + 7 < 28/3, then subtract 7 to find m < 7/3.

Front

What is the importance of flipping the inequality sign when dividing by a negative number?

Back

Flipping the inequality sign is necessary because dividing or multiplying both sides of an inequality by a negative number reverses the order of the values.

Front

What are the steps to solve a 2-step inequality?

Back

1. Isolate the term with the variable by adding or subtracting. 2. Divide or multiply to solve for the variable, remembering to flip the inequality sign if dividing by a negative.

Front

What does it mean if an inequality has no solution?

Back

An inequality has no solution when the variable cannot satisfy the inequality, such as when simplifying leads to a false statement like 5 < 3.

Front

What is the graphical representation of an inequality?

Back

The graphical representation of an inequality is a number line where the solution set is shown with an open or closed circle and a shaded region indicating all possible solutions.