Solving Two-Step Inequalities: Key Concepts and Examples

The video tutorial covers solving two-step inequalities, emphasizing the importance of inverse operations and switching inequality symbols when multiplying or dividing by negative numbers. It provides four examples, demonstrating step-by-step solutions and graphing the results. The tutorial highlights efficient problem-solving techniques, such as simplifying expressions before solving.

What must you remember to do when you multiply or divide both sides of an inequality by a negative number?

• Subtract the same number from both sides

• Switch the inequality symbol

• Add the same number to both sides

• Keep the inequality symbol the same

What is the first step in solving the inequality 6x - 7 ≥ 35?

• Multiply both sides by 6

• Subtract 7 from both sides

• Add 7 to both sides

• Divide both sides by 6

After adding 7 to both sides of the inequality 6x - 7 ≥ 35, what is the resulting inequality?

• 6x ≥ 42

• 6x ≥ 28

• 6x ≤ 42

• 6x ≤ 28

What type of circle is used to graph the solution x ≥ 7?

• No circle

• Half-filled circle

• Closed circle

• Open circle

What is the first step in solving the inequality w / -4 + 3 ≥ -6?

• Add 3 to both sides

• Multiply both sides by -4

• Divide both sides by -4

• Subtract 3 from both sides

When solving w / -4 + 3 ≥ -6, what must you do after multiplying both sides by -4?

• Switch the inequality symbol

• Keep the inequality symbol the same

• Subtract 4 from both sides

• Add 4 to both sides

What is the first step in solving the inequality -5(x + 9) < 30?

• Divide both sides by -5

• Subtract 9 from both sides

• Add 9 to both sides

• Distribute -5 to x and 9

After dividing both sides of -5(x + 9) < 30 by -5, what is the resulting inequality?

• x + 9 > 6

• x + 9 < 6

• x + 9 > -6

• x + 9 < -6

What is the simplified form of the inequality 7x + 32 - 9x ≤ 27 - 13?

• 32 - 2x ≤ 14

• 32 + 2x ≤ 14

• 32 + 2x ≥ 14

• 32 - 2x ≥ 14

What is the final solution to the inequality 7x + 32 - 9x ≤ 27 - 13?

• x ≤ -9

• x ≥ -9

• x ≤ 9

• x ≥ 9