Solving Inequalities and Graphing Solutions

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 several examples demonstrating different scenarios, such as having variables on both sides, using the distributive property, and dealing with parentheses. The video emphasizes the importance of graphing solutions on a number line and provides tips for avoiding common mistakes.

What is the main difference between solving equations and inequalities?

• Equations have solutions like x = 1, while inequalities have solutions like x > 1.

• Equations and inequalities are solved using different operations.

• Equations require graphing, while inequalities do not.

• Inequalities always have negative solutions.

Why is it important to get variables on the same side of an inequality?

• To avoid using inverse operations.

• To ensure the inequality has no solution.

• To simplify the inequality and solve it more easily.

• To make the inequality more complex.

What should you do when you multiply or divide by a negative number in an inequality?

• Flip the inequality sign.

• Subtract a constant from both sides.

• Keep the inequality sign the same.

• Add a constant to both sides.

In the example 21x + 7 < 3x + 16, what is the first step to solve the inequality?

• Add 21x to both sides.

• Subtract 3x from both sides.

• Multiply both sides by 2.

• Divide both sides by 7.

How do you represent the solution x < 1/2 on a number line?

• With an open circle at 1/2 and shading to the right.

• With an open circle at 1/2 and shading to the left.

• With a closed circle at 1/2 and shading to the right.

• With a closed circle at 1/2 and shading to the left.

In the example 18 <= 7x + 4, what operation should be performed first?

• Multiply both sides by 7.

• Add 4 to both sides.

• Divide both sides by 7.

• Subtract 4 from both sides.

How is the solution 2 <= x represented on a number line?

• With a closed circle at 2 and shading to the left.

• With a closed circle at 2 and shading to the right.

• With an open circle at 2 and shading to the right.

• With an open circle at 2 and shading to the left.

What is the first step in solving 2x - 8 > 4x + 6?

• Divide both sides by 2.

• Add 8 to both sides.

• Subtract 4x from both sides.

• Apply the distributive property.

How do you graph the solution x < 7 on a number line?

• With an open circle at 7 and shading to the right.

• With an open circle at 7 and shading to the left.

• With a closed circle at 7 and shading to the right.

• With a closed circle at 7 and shading to the left.

In the example 4x - 2 <= -6x - 9, what should be done first?

• Subtract 2 from both sides.

• Multiply both sides by 4.

• Divide both sides by 9.

• Add 6x to both sides.