Inequalities and Their Solutions

The video tutorial explains how to solve and graph an inequality. It begins by setting up the inequality and treating it like an equation, except when multiplying or dividing by a negative number. The distributive property is applied to simplify the expression, and variables are isolated. The solution is found by solving for the variable b, and the importance of flipping the inequality sign when dividing by a negative number is highlighted. Finally, the solution is graphed on a number line, and the process of determining which side of the point to shade is explained.

What is the initial inequality presented in the problem?

• 11b + 10 ≤ 9b - 10

• -11b + 10 ≤ 9b - 10

• -11b + 10 ≥ 9b - 10

• 11b - 10 ≤ 9b + 10

What property is applied to simplify the inequality?

• Identity Property

• Associative Property

• Commutative Property

• Distributive Property

After applying the distributive property, what is the resulting expression?

• -11b - 110 ≤ 9b - 90

• -11b + 110 ≥ 9b + 90

• -11b + 110 ≤ 9b + 90

• -11b - 110 ≥ 9b - 90

What operation is performed to isolate the variable b?

• Adding 110

• Dividing by 20

• Subtracting 9b

• Multiplying by -20

What is the inequality after isolating the variable b?

• -20b ≤ 20

• -20b ≥ 20

• 20b ≤ -20

• 20b ≥ -20

Why is it important to flip the inequality sign when dividing by a negative number?

• It ensures the inequality remains true.

• It is not necessary to flip the sign.

• It is a rule for equations.

• It simplifies the calculation.

What is the final solution for b after solving the inequality?

• b ≥ -1

• b ≤ -1

• b ≤ 1

• b ≥ 1

Where is the point plotted on the number line for the solution b ≥ -1?

• At 0

• At -1

• At -2

• At 1

Which direction is the shading on the number line for the solution b ≥ -1?

• Both directions

• To the right

• No shading

• To the left

What is the purpose of testing points like 2 and -2 in the solution?

• To verify the inequality sign

• To determine the midpoint

• To find the exact solution

• To check the accuracy of the graph