Mastering Multi-Step Inequalities with Variables

The video tutorial from Friendly Math 101 covers solving multi-step inequalities with variables on both sides. It explains the process, which is similar to solving equations, and provides two examples. The first example demonstrates solving and graphing an inequality, while the second example includes additional steps and graphing. Key points include distributing, combining like terms, and ensuring the inequality symbol is correctly maintained or flipped when necessary. The tutorial concludes with important tips and encourages viewers to subscribe for more math tutorials.

What is the first step in solving multi-step inequalities with variables on both sides?

• Distribute and combine like terms

• Move all variables to one side

• Divide by the coefficient of the variable

• Graph the inequality

What is the significance of the inequality symbol in the context of these problems?

• It has no significance; it can be ignored

• It changes the steps for solving the inequality

• It determines the method of distribution

• It indicates the direction of the graph on the number line

In the first example, after combining like terms and distributing, what is the next step?

• Move all variables to one side

• Multiply or divide by the coefficient of the variable

• Graph the solution

• Add or subtract to isolate the variable

What is the final solution for the inequality in the first example?

• x < 3

• x < 4

• x > 4

• x > 3

How do you represent a solution that does not include the endpoint on a number line?

• With a closed circle

• With an open circle

• By shading the entire number line

• By drawing a line through the number

In the second example, what is the correct way to solve for x after combining like terms and distributing?

• Add or subtract from both sides

• Move all constants to one side

• Multiply or divide both sides by the coefficient of x

• Graph the inequality

When solving inequalities, if you multiply or divide by a negative number, what should you do to the inequality symbol?

• Leave it unchanged

• Flip the symbol

• Replace it with an equal sign

• Remove the symbol

How is the solution 'x is less than or equal to 3' represented on a number line?

• With an open circle on 3 and shading to the left

• With a closed circle on 3 and shading to the right

• With an open circle on 3 and shading to the right

• With a closed circle on 3 and shading to the left

After solving the inequality in the second example, how do you graph '3 is greater than or equal to x'?

• Place a closed circle on 3 and shade to the right

• Place an open circle on 3 and shade to the left

• Place a closed circle on 3 and shade to the left

• Place an open circle on 3 and shade to the right

Why is it important to remember to flip the inequality symbol when multiplying or dividing by a negative number?

• It has no impact on the solution

• It is only a suggestion, not a rule

• It ensures the solution set is accurate

• It makes the problem easier to solve