Exploring Rational Expressions in Lesson 3.6

In this lesson, students learn to solve multi-step inequalities by combining knowledge of equations and inequalities. The video reviews key concepts, provides step-by-step examples, and offers practice problems. It emphasizes the importance of flipping the inequality sign when multiplying or dividing by a negative number and includes strategies for checking solutions.

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

• Subtract 1 from it

• Flip it

• Leave it unchanged

• Add 1 to it

In the inequality x/(-4) - 6 ≥ -5, what is the first step to isolate x?

• Divide both sides by -4

• Multiply both sides by -4

• Subtract 6 from both sides

• Add 6 to both sides

After isolating x in the inequality x/(-4) - 6 ≥ -5, what should you do next?

• Multiply both sides by -4 and flip the inequality sign

• Divide both sides by 4 and keep the inequality sign

• Divide both sides by -4 and flip the inequality sign

• Multiply both sides by 4 and keep the inequality sign

When graphing the solution to x ≤ -4, what type of circle should be used at -4?

• Half-filled circle

• No circle

• Closed circle

• Open circle

In the inequality 4x + 1 > 9, what is the first step to isolate x?

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply both sides by 4

• Divide both sides by 4

After isolating x in the inequality 4x + 1 > 9, what should you do next?

• Multiply both sides by 4

• Divide both sides by 4

• Add 1 to both sides

• Subtract 1 from both sides

When solving an inequality with variables on both sides, what is a good strategy to keep the coefficient of the variable positive?

• Add the larger variable term to both sides

• Subtract the larger variable term from both sides

• Add the smaller variable term to both sides

• Subtract the smaller variable term from both sides

In the inequality 5y + 2 ≤ y + 34, what is the first step to isolate y?

• Add y to both sides

• Subtract y from both sides

• Add 2 to both sides

• Subtract 2 from both sides

When graphing the solution to y ≤ 8, what type of circle should be used at 8?

• Half-filled circle

• Open circle

• Closed circle

• No circle

What should you always do after solving an inequality to ensure your solution is correct?

• Rewrite the inequality

• Graph the solution

• Check the solution by substituting back into the original inequality

• Multiply both sides by a positive number