Rearranging Inequalities into y = mx + b Form

The video tutorial covers rearranging equations into the y=mx+b form, focusing on inequalities. It explains the process of isolating y, handling terms with x, and the importance of flipping the inequality sign when dividing by a negative number. Several examples are provided to illustrate these concepts, including cases where the sign does not flip due to division by a positive number.

What is the additional step required when rearranging equations into y = mx + b form with inequalities?

• Changing the variable y to x

• Adding a constant to both sides

• Flipping the inequality sign when dividing by a negative

• Multiplying all terms by zero

When isolating y, why can't terms with x be combined with constant terms?

• Because they are on different sides of the equation

• Because they have different coefficients

• Because one term has x and the other does not

• Because they are both negative

What happens to the inequality sign when you divide all terms by a negative number?

• It flips direction

• It stays the same

• It disappears

• It becomes an equal sign

In the process of rearranging, what should you do if you want to change a negative y to a positive y?

• Subtract y from both sides

• Add a constant to both sides

• Multiply by zero

• Divide by negative one

In the example with -19x, what is the result after dividing by negative one?

• y is greater than or equal to -19x - 3

• y is less than -19x - 3

• y is less than or equal to 19x + 3

• y is greater than 19x + 3

When dividing by a positive number, what happens to the inequality sign?

• It flips direction

• It disappears

• It stays the same

• It becomes an equal sign

In the example 3x + 8y ≥ 13, what is the final form after rearranging?

• y ≥ -3/8x - 13/8

• y ≤ 3/8x + 13/8

• y ≥ 3/8x + 13/8

• y = 3/8x - 13/8

What is the result of dividing -10x + 16 by -2 in the final example?

• 5x - 8

• -5x + 8

• 5x + 8

• -5x - 8

Why is it important to remember the direction of the inequality sign when rearranging equations?

• Because it affects the coefficients

• Because it alters the constants

• Because it changes the variable

• Because it determines the solution set

What is the final form of the inequality 10x - 2y < 16 after rearranging?

• y > 5x - 8

• y < 5x - 8

• y = 5x + 8

• y > -5x + 8