Understanding Inequalities and Graphing Solutions

The video tutorial explains how to solve the inequality -5c ≤ 15 for c. It involves isolating c by multiplying both sides by the inverse of -5, which requires flipping the inequality sign. The solution, c ≥ -3, is then graphed on a number line. The tutorial concludes by verifying the solution with examples, ensuring the correct values are included in the solution set.

What is the initial inequality that needs to be solved?

• 5c ≥ 15

• 5c ≤ 15

• -5c ≥ 15

• -5c ≤ 15

What operation is used to isolate c in the inequality -5c ≤ 15?

• Divide both sides by 5

• Multiply both sides by -1/5

• Subtract 5 from both sides

• Add 5 to both sides

What must be done to the inequality sign when multiplying both sides by a negative number?

• Double it

• Remove it

• Flip it

• Keep it the same

What is the solution to the inequality -5c ≤ 15?

• c ≥ 3

• c ≤ -3

• c ≥ -3

• c ≤ 3

On a number line, which value is included in the solution set for c?

• -4

• 0

• -3

• 3

Which of the following values satisfies the original inequality -5c ≤ 15?

• 5

• 4

• 0

• -4

What happens when you test the value -4 in the inequality -5c ≤ 15?

• It satisfies the inequality

• It does not satisfy the inequality

• It equals the inequality

• It reverses the inequality

What is the result of multiplying -5 by 0 in the context of the inequality?

• 15

• 5

• 0

• -5

Why is it important to verify the solution of an inequality?

• To change the inequality

• To find a new solution

• To simplify the inequality

• To ensure the solution is correct

What does the filled circle on the number line represent in the graph of the solution?

• The endpoint of the solution

• The midpoint of the solution

• A value included in the solution

• A value not included in the solution