Master Solving and Graphing multi step inequalities

The video tutorial explains how to solve and graph multi-step inequalities. It covers the process of treating inequalities like equations, using inverse operations, and the importance of flipping the inequality sign when multiplying or dividing by a negative number. The tutorial includes examples of solving inequalities and graphing their solutions on a number line, emphasizing the need to keep variables positive to avoid errors. Advanced examples demonstrate handling inequalities with parentheses.

What is a key difference between solving equations and inequalities?

• Inequalities require a graph for solutions.

• Equations always have multiple solutions.

• Inequalities do not use inverse operations.

• Equations require flipping the sign when dividing by a negative.

Why is it important to keep the variable's coefficient positive when solving inequalities?

• To avoid using a number line.

• To simplify the equation.

• To prevent flipping the inequality sign.

• To ensure the solution is an integer.

What should you do if you have a negative coefficient while solving an inequality?

• Always divide by the negative number.

• Flip the inequality sign.

• Add a positive number to both sides.

• Ignore the negative sign.

When graphing the solution x < 1/2 on a number line, what should you do?

• Shade to the right of 1/2.

• Use an open circle at 1/2.

• Shade only at 1/2.

• Use a closed circle at 1/2.

When is it necessary to flip the inequality sign?

• When adding a negative number.

• When multiplying or dividing by a negative number.

• When subtracting a positive number.

• When the variable is on the right side.

How can you represent a non-integer solution on a number line?

• Use a closed circle.

• Use an open circle.

• Use a shaded region.

• Use a dashed line.

What is a common mistake when graphing inequalities with variables on the right side?

• Not rewriting the inequality for easier graphing.

• Using a closed circle for all inequalities.

• Forgetting to use a number line.

• Always shading to the left.

What is the benefit of rewriting an inequality with the variable on the left side?

• It changes the solution.

• It makes graphing easier.

• It simplifies the inequality.

• It eliminates the need for a number line.

How do you handle parentheses in multi-step inequalities?

• Ignore them and solve directly.

• Apply the distributive property first.

• Move them to the other side of the inequality.

• Solve the inequality without simplifying.

What should you do if both sides of an inequality have parentheses?

• Ignore the parentheses.

• Apply the distributive property to both sides.

• Solve each side separately.

• Combine the terms inside the parentheses.