Solving Inequalities with Variables on Both Sides

In this video, Mr. J explains how to solve inequalities with variables on both sides. He demonstrates two methods: one that avoids negative coefficients and another that moves variables to the left side. The video emphasizes the importance of flipping the inequality symbol when dividing by a negative number. Mr. J verifies the solution by substituting a value and concludes with a summary of the process.

What is the first step in solving inequalities with variables on both sides?

• Get the variable on one side of the inequality

• Multiply both sides by a negative number

• Divide both sides by a positive number

• Add a constant to both sides

When solving inequalities, what happens to the inequality symbol when you multiply or divide both sides by a negative number?

• It disappears

• It remains the same

• It flips direction

• It becomes an equal sign

In the first method, why do we subtract 2x from both sides?

• To avoid a negative coefficient

• To add complexity to the problem

• To eliminate the variable

• To make the equation simpler

What is the result of dividing -20 by 4 in the first method?

• 4

• 5

• -5

• -4

How can you rewrite an inequality to have the variable first?

• By adding a constant to both sides

• By writing the variable first and ensuring the inequality symbol is correct

• By flipping the inequality symbol

• By changing the variable

In the second method, what is the first step to get the variable on the left side?

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 6X from both sides

• Add 6X to both sides

Why is it important to flip the inequality symbol in the second method?

• Because we are adding a positive number

• Because we are dividing by a negative number

• Because we are subtracting a positive number

• Because we are multiplying by a positive number

What is the final solution for X in both methods?

• X is less than -5

• X is greater than -5

• X is equal to -5

• X is not equal to -5

What value is used to verify the solution in the final section?

• 0

• 5

• 10

• -5

What is the result of substituting 0 into the original inequality?

• 13 is less than 7

• 0 is equal to 13

• 7 is greater than 13

• -7 is less than 13