Solving Inequalities and Their Properties

This video tutorial by Mr. J covers solving two-step inequalities through four examples. It explains the process of isolating the variable using inverse operations, similar to solving two-step equations. The video 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 primary goal when solving two-step inequalities?

• To isolate the variable on one side of the inequality

• To convert the inequality into an equation

• To find the exact value of the variable

• To eliminate all variables

When solving the inequality 7X - 3 > 18, what is the first step?

• Add 3 to both sides

• Multiply both sides by 7

• Divide both sides by 3

• Subtract 7 from both sides

In the inequality 7X - 3 > 18, what is the solution for X?

• X = 3

• X < 3

• X >= 3

• X > 3

What happens to the inequality symbol when both sides are multiplied or divided by a negative number?

• It becomes an equation

• It flips direction

• It remains the same

• It is removed

In the inequality y / -2 + 5 >= 9, what is the solution for y?

• y <= 8

• y > 8

• y >= 8

• y < 8

When solving -4n + 6 >= -14, what is the first operation to perform?

• Multiply both sides by -4

• Divide both sides by -4

• Subtract 6 from both sides

• Add 6 to both sides

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 both sides by 9

• Divide both sides by 9

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

• m < 99

• m > 99

• m = 99

• m >= 99

Why might you rewrite an inequality with the variable first?

• To make it look more complex

• To simplify the inequality

• To make it easier to interpret

• To change the solution