Solving Two-Step Inequalities in Algebra

The video tutorial explains how to solve an inequality involving fractions and mixed numbers. It begins by converting mixed numbers to improper fractions, then eliminates fractions by multiplying both sides of the inequality. The tutorial continues by simplifying the inequality and isolating the variable y. Finally, it interprets the solution and demonstrates how to represent it on a number line.

What is the first step in solving the inequality 2/3 > -4y - 8 1/3?

• Add 8 1/3 to both sides

• Multiply both sides by 3

• Convert 8 1/3 to an improper fraction

• Subtract 2/3 from both sides

What is 8 1/3 converted to an improper fraction?

• 25/3

• 27/3

• 26/3

• 24/3

Why do we multiply both sides of the inequality by 3?

• To swap the inequality sign

• To make the inequality simpler

• To eliminate the fractions

• To isolate the variable

What happens to the inequality sign when you multiply both sides by a positive number?

• It disappears

• It becomes an equal sign

• It remains the same

• It swaps

What is the result of multiplying 3 by 2/3?

• 1

• 2

• 3

• 4

What is the next step after simplifying the inequality to 27 > -12y?

• Add 12y to both sides

• Subtract 27 from both sides

• Multiply both sides by -12

• Divide both sides by -12

What must you do to the inequality sign when dividing both sides by a negative number?

• Remove it

• Turn it into an equal sign

• Swap it

• Leave it unchanged

What is the simplified form of 27 divided by -12?

• -27/12

• -3/2

• -9/4

• -2 1/4

How can you express -9/4 as a mixed number?

• -2 1/3

• -2 1/4

• -2 1/2

• -2 1/5

How is the solution y > -2 1/4 represented on a number line?

• An open circle at -2 1/4 with shading to the left

• A closed circle at -2 1/4 with shading to the left

• An open circle at -2 1/4 with shading to the right

• A closed circle at -2 1/4 with shading to the right