Inequalities and Their Solutions

The video tutorial explains how to solve inequalities involving fractions. It covers two examples: the first involves multiplying both sides by the least common denominator to eliminate fractions, while the second involves handling negative multiplication, which requires reversing the inequality sign. The tutorial emphasizes the importance of checking solutions on a number line and understanding the impact of multiplying or dividing by negative numbers.

What is the first step in solving inequalities involving fractions?

• Add the fractions directly.

• Multiply both sides by the least common denominator.

• Subtract the fractions.

• Divide both sides by the largest denominator.

What is the least common denominator used in the first inequality problem?

• 10

• 6

• 5

• 3

What is the result of simplifying 3x - 2x?

• 0

• 5x

• x

• 2x

What is the result of simplifying 10 + 15?

• 30

• 25

• 35

• 20

In the first inequality problem, what is the solution for X?

• X ≤ 25

• X = 25

• X > 25

• X < 25

How do you represent the solution X > 25 on a number line?

• Shade the area including 25.

• Shade the area to the left of 25.

• Do not shade any area.

• Shade the area to the right of 25.

What is the first step in solving the second inequality problem?

• Divide by the largest number

• Add fractions

• Take numbers together and variables on one side

• Multiply everything by 3

When multiplying or dividing by a negative number in an inequality, what must you remember to do?

• Add 1 to both sides.

• Keep the inequality sign the same.

• Subtract 1 from both sides.

• Reverse the inequality sign.

In the second inequality, what operation is performed after simplifying the numerator?

• Multiplication by negative 2

• Division by 2

• Subtraction

• Addition

What is the result of multiplying -2 by -x/2?

• -2x

• 2x

• -x

• x