Solving Inequalities and Isolating Variables

This video tutorial by Mr. J covers how to solve two-step inequalities through four examples. It explains the process of isolating the variable using inverse operations, similar to solving two-step equations. The tutorial emphasizes the importance of flipping the inequality symbol when multiplying or dividing by a negative number. Each example is solved step-by-step, demonstrating the application of these principles and verifying the solutions by plugging in values.

What is the first step in solving a two-step inequality?

• Add a constant to both sides

• Isolate the variable using inverse operations

• Multiply both sides by a negative number

• Flip the inequality symbol

When solving the inequality 7X - 3 > 18, what operation should be performed first?

• Subtract 3

• Multiply by 7

• Divide by 7

• Add 3

After isolating X in the inequality 7X - 3 > 18, what is the solution for X?

• X < 3

• X > 3

• X >= 3

• X = 3

In the inequality y / -2 + 5 >= 9, why do we flip the inequality symbol?

• Because we divide by a positive number

• Because we multiply by a negative number

• Because we subtract a positive number

• Because we add a positive number

What is the solution for y in the inequality y / -2 + 5 >= 9?

• y > 8

• y < 8

• y >= 8

• y <= 8

In the inequality -4n + 6 >= -14, what operation is used to isolate n?

• Add 6

• Multiply by -4

• Subtract 6

• Divide by -4

What is the solution for n in the inequality -4n + 6 >= -14?

• n >= 5

• n < 5

• n <= 5

• n > 5

In the inequality 3 > m / 9 - 8, what is the first step to isolate m?

• Subtract 8 from both sides

• Add 8 to both sides

• Multiply by 9

• Divide by 9

What is the solution for m in the inequality 3 > m / 9 - 8?

• m > 99

• m < 99

• m <= 99

• m = 99

How can an inequality be rewritten to make it easier to work with?

• By adding a constant to both sides

• By changing the inequality symbol

• By writing the variable first

• By multiplying both sides by a negative