Inequalities and Their Solutions

This video tutorial teaches how to solve inequalities in one variable with negative coefficients. It explains the process of dividing by a negative number and changing the direction of the inequality sign. The tutorial includes example problems to illustrate the concept, showing how to handle negative coefficients and verify solutions. By the end, viewers will understand how to solve such inequalities and check their solutions.

What is the first step in solving an inequality with a negative coefficient?

• Multiply by a positive number

• Divide by a negative number and change the inequality direction

• Add a positive number to both sides

• Subtract a negative number from both sides

In the inequality -5x + 7 ≥ 12, what is the correct solution for x?

• x ≤ 1

• x ≥ -1

• x ≤ -1

• x ≥ 1

Why do we change the direction of the inequality sign when multiplying by a negative number?

• To eliminate negative numbers

• To ensure the inequality remains true

• To simplify the expression

• To make the inequality easier to solve

What is the result of distributing a negative over the inequality -5x + 7 ≥ 12?

• -5x + 7 ≤ 12

• 5x + 7 ≥ -12

• -5x - 7 ≤ 12

• 5x - 7 ≤ -12

In the inequality 10 - 3x > 37, what is the solution for x after taking the opposite of each term?

• x > 9

• x < 9

• x < -9

• x > -9

What is the correct inequality after adding 10 to both sides of -10 + 3x < -37?

• 3x < -27

• 3x > -27

• 3x > 27

• 3x < 27

When solving 10 - 3x > 37, why do we place an open circle over -9?

• Because -9 is the maximum value

• Because -9 is included in the solution

• Because -9 is the only solution

• Because -9 is not included in the solution

What is the result of checking the inequality 10 - 3x > 37 with x = -10?

• 37 < 40, which is incorrect

• 37 > 40, which is correct

• 40 < 37, which is incorrect

• 40 > 37, which is correct

What is the key takeaway from solving inequalities with negative coefficients?

• Never change the inequality direction

• Change the direction of the inequality when dividing by a negative

• Always subtract a negative number from both sides

• Always add a positive number to both sides

What happens to the inequality sign when you multiply or divide by a negative number?

• It becomes undefined

• It becomes an equality

• It changes direction

• It stays the same