Solving Inequalities with Variables on Both Sides

This video tutorial covers solving inequalities with variables on both sides. It begins with an introduction to the concept, emphasizing the importance of maintaining the direction of the inequality sign when multiplying or dividing by a negative number. The tutorial then provides detailed solutions to several examples, demonstrating how to simplify and solve inequalities. It also discusses how to determine if inequalities are always, sometimes, or never true. Finally, the video applies these concepts to a real-world scenario involving cell phone usage, illustrating the practical application of inequalities.

What must be done to both sides of an inequality when performing operations?

• Only add or subtract on one side

• Ignore operations on the negative side

• Perform different operations on each side

• Perform the same operation on both sides

Tags

CCSS.6.EE.B.8

What happens to the inequality sign when multiplying or dividing by a negative number?

• It becomes an equality sign

• It is reversed

• It disappears

• It remains unchanged

Tags

CCSS.6.EE.B.8

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

• Isolate the variable on one side

• Multiply both sides by the variable coefficient

• Add the variable terms from both sides

• Divide both sides by the variable coefficient

In the context of inequalities, what does adding 2x to both sides accomplish?

• It doubles the x coefficient

• It balances the equation

• It eliminates the x term from the equation

• It removes the x term from one side

When solving inequalities involving fractions, what should you multiply by?

• The largest coefficient in the equation

• The least common multiple of the denominators

• Any common multiple of the denominators

• The highest exponent in the equation

What is the result of multiplying all terms by 10 in an inequality with fractions?

• It simplifies the inequality by clearing fractions

• It makes the inequality more complex

• It changes the direction of the inequality

• It has no effect on the inequality

Tags

CCSS.6.EE.B.8

What is a crucial step when you have like terms on both sides of an inequality?

• Divide each term by the coefficient

• Combine like terms to simplify the inequality

• Subtract the smaller term from the larger

• Multiply each term by the coefficient

What does adding 5x to both sides of an inequality typically achieve?

• It simplifies the constants in the inequality

• It changes the inequality to an equality

• It cancels out x terms on one side

• It introduces new variables

How do you determine if an inequality is always true?

• If it simplifies to a true statement regardless of variable value

• If it contains multiple variables

• If it only holds under certain conditions

• If it simplifies to a false statement

Tags

CCSS.8.EE.C.7A

In a real-world scenario, how can you use inequalities to predict future outcomes?

• By using inequalities to model potential changes

• By ignoring past trends

• By guessing future trends

• By setting up equations based on past data