Solving and Graphing Inequalities

The video tutorial explains how to solve multi-step inequalities. It begins with an introduction to the distributive property and the importance of applying it correctly. The teacher then demonstrates how to combine like terms to simplify the inequality. The process of solving the inequality for a single variable is detailed, emphasizing the need to flip the inequality sign when dividing by a negative number. Finally, the tutorial covers graphing the solution on a number line, highlighting how to determine which side of the line to shade based on the inequality.

What is the first step in solving a multi-step inequality?

• Combine like terms

• Test points on a number line

• Apply the distributive property

• Graph the solution

When applying the distributive property, what should you do with the number outside the parentheses?

• Multiply it by each term inside

• Add it to each term inside

• Subtract it from each term inside

• Divide it by each term inside

What is the result of applying the distributive property to 4(8 - 2b)?

• 32 - 8b

• 32 + 8b

• 4 - 2b

• 8 - 2b

How do you combine the terms -8b and -2b?

• Add them to get -6b

• Subtract them to get -10b

• Subtract them to get -6b

• Add them to get -10b

What is the next step after combining like terms in an inequality?

• Graph the solution

• Isolate the variable

• Test points on a number line

• Apply the distributive property again

What must you remember when dividing both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Flip the inequality sign

• Keep the inequality sign the same

What is the solution to the inequality -10b ≤ 0 after solving for b?

• b ≥ 0

• b ≤ 0

• b > 0

• b < 0

What is the result of solving the inequality 32 - 10b ≤ 32?

• b < 0

• b > 0

• b ≤ 0

• b ≥ 0

How do you represent the solution b ≥ 0 on a number line?

• Do not shade at all

• Shade to the left of 0

• Shade to the right of 0

• Shade both sides of 0

What does shading to the right of 0 on a number line indicate?

• All points are less than or equal to 0

• All points are greater than or equal to 0

• All points are less than 0

• All points are equal to 0