Solving Linear Inequalities

The video tutorial explains how to solve the inequality 2 - 3x < 14. It begins by treating the inequality like a regular algebraic equation, emphasizing the need to flip the inequality sign when multiplying or dividing by a negative number. The tutorial walks through the steps of isolating x, subtracting 2 from both sides, and dividing by -3, resulting in the solution x > -4.

What is the initial inequality given in the problem?

• 3x - 2 < 14

• 2 - 3x < 14

• 3x + 2 > 14

• 2 - 3x > 14

What is the main goal when solving the inequality 2 - 3x < 14?

• To prove the inequality is false

• To determine the range of possible values for x

• To find the exact value of x

• To rewrite the inequality in a different form

What special rule must be remembered when dealing with inequalities and negative numbers?

• Ignore the negative sign

• Always add a positive number

• Flip the inequality sign when multiplying or dividing by a negative number

• Subtract a negative number

What is the first step in isolating x in the inequality 2 - 3x < 14?

• Add 3 to both sides

• Subtract 2 from both sides

• Multiply both sides by 3

• Divide both sides by 2

After subtracting 2 from both sides, what does the inequality become?

• 3x < 12

• -3x > 12

• 3x > 12

• -3x < 12

What is the first step in solving the inequality 2 - 3x < 14?

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply by -3

• Divide by 3

What is the result of subtracting 2 from both sides of the inequality?

• 3x > 12

• -3x > 12

• -3x < 12

• 3x < 12

Why is it important to flip the inequality sign when dividing by a negative number?

• To change the direction of the inequality

• To make the inequality easier to solve

• To ensure the solution is correct

• To keep the inequality balanced

What operation is performed after obtaining -3x < 12?

• Subtract 3

• Divide by -3

• Multiply by 3

• Add 3

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

• It flips direction

• It stays the same

• It becomes an equal sign

• It is removed