Solving Two-Step Inequalities

In this math class video, students learn to solve two-step inequalities by treating them like equations, with the key difference being the absence of an equal sign. The video explains the process of solving inequalities, including when to flip the inequality sign when multiplying or dividing by a negative number. It also covers graphing inequalities on a number line using open and closed circles, and methods to verify solutions. The lesson concludes with encouragement to practice and a reminder to pay attention to the rules for flipping inequality signs.

What is the main difference between an equation and an inequality?

• Inequalities have an equal sign.

• Equations have less than or greater than signs.

• Equations do not have variables.

• Inequalities do not have an equal sign.

What is the first step in solving the inequality -6y + 3 ≥ 0?

• Divide both sides by -6.

• Multiply both sides by -6.

• Subtract 3 from both sides.

• Add 3 to both sides.

After subtracting 3 from both sides of the inequality -6y + 3 ≥ 0, what is the next step?

• Multiply both sides by -6.

• Subtract 6 from both sides.

• Add 6 to both sides.

• Divide both sides by -6.

Why do we flip the inequality sign when dividing by a negative number?

• Because it is a rule that must be memorized.

• Because it makes the inequality easier to solve.

• Because dividing by a negative number changes the direction of the inequality.

• Because it simplifies the inequality.

What type of circle is used on a number line for a 'less than' or 'greater than' inequality?

• Dotted circle

• Shaded circle

• Open circle

• Closed circle

What type of circle is used on a number line for a 'less than or equal to' or 'greater than or equal to' inequality?

• Shaded circle

• Open circle

• Dotted circle

• Closed circle

If y ≤ 1/2, which direction should you shade on the number line?

• Both directions

• To the left

• To the right

• Do not shade

How can you check if a solution is correct for an inequality?

• By flipping the inequality sign.

• By substituting the value into the inequality.

• By adding the same number to both sides.

• By graphing the inequality.

What should you do if you multiply or divide both sides of an inequality by a negative number?

• Keep the inequality sign the same.

• Add the same number to both sides.

• Subtract the same number from both sides.

• Flip the inequality sign.

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

• To indicate the range of possible solutions.

• To make the graph look better.

• To confuse the viewer.

• To show the exact solution.