Exploring 4-4 Inequalities with Variables on Both Sides

The video tutorial covers solving inequalities with variables on both sides, emphasizing the use of the distributive property, combining like terms, and determining solution sets on a number line. It provides step-by-step examples, including handling cases with and without parentheses, and explains how to manipulate equations to isolate variables and find solutions.

What is the first step when solving an inequality with variables on both sides?

• Combine like terms

• Distribute any constants

• Flip the inequality symbol

• Add the same number to both sides

When simplifying 2 times 6 and 2 times -5x, what do you get?

• 12 and -10x

• 10 and -10x

• 10 and -12x

• 12 and -8x

What does a closed circle on a number line represent?

• The number is not included in the solution

• The inequality is strict

• The number is included in the solution

• The inequality is not strict

In the inequality 10 + 2x ≥ 12, what is the next step after adding 10x to both sides?

• Add 12 to both sides

• Multiply by 2

• Divide by 2

• Subtract 10 from both sides

What is the solution to the inequality 2x > -6?

• x > -3

• x < -3

• x > 3

• x < 3

What does an open circle on a number line indicate?

• The inequality is not strict

• The number is included in the solution

• The number is not included in the solution

• The inequality is strict

When distributing 3 to the terms inside the parentheses, what do you get?

• 18 and -12a

• 18 and -4a

• 6 and -12a

• 6 and -4a

What is the solution to the inequality a ≥ 2?

• a > 2

• a < 2

• a ≥ 2

• a ≤ 2

In the inequality 1m - 5 > 7, what is the next step after subtracting 5m from both sides?

• Subtract 5 from both sides

• Add 5 to both sides

• Multiply by 5

• Divide by 5

What is the solution to the inequality m > 12?

• m ≥ 12

• m > 12

• m < 12

• m ≤ 12