Solving Inequalities and Graphing

This video tutorial covers solving and graphing multi-step inequalities. It explains the process of solving inequalities, highlighting the importance of changing the inequality sign when multiplying or dividing by negative numbers. The tutorial also demonstrates how to graph inequalities on a number line, using examples to illustrate the steps involved. Key concepts include the distributive property, combining like terms, and the impact of negative coefficients on inequality signs.

What is the main similarity between solving equations and solving inequalities?

• Both involve only addition and subtraction.

• Both involve changing the inequality sign.

• Both follow the same steps except for the inequality sign.

• Both require graphing the solution.

When solving inequalities, what happens to the inequality sign when you multiply or divide by a negative number?

• It changes to an equal sign.

• It stays the same.

• It becomes a positive sign.

• It flips direction.

In the example where -3x > 15, what is the first step to isolate x?

• Divide both sides by -3.

• Add 3 to both sides.

• Multiply both sides by 3.

• Subtract 15 from both sides.

What is the purpose of placing a circle on the number line when graphing an inequality?

• To indicate the midpoint of the line.

• To mark the end of the graph.

• To show the starting point of the graph.

• To represent the value in the inequality.

How do you determine whether to use an open or closed circle when graphing an inequality?

• Open for greater than or less than, closed for equal to.

• Closed for greater than or less than, open for equal to.

• Open for equal to, closed for greater than or less than.

• It doesn't matter; use either.

In Example 1, what is the first step in solving the inequality 5(x - 4) + 3x ≤ 12x - 40 - 2x?

• Subtract 3x from both sides.

• Distribute 5 into (x - 4).

• Combine like terms.

• Add 40 to both sides.

In Example 2, why is it important to flip the inequality sign when dividing by a negative number?

• To ensure the solution is correct.

• To keep the inequality balanced.

• To avoid negative solutions.

• To make the equation easier to solve.