Understanding Inequalities and Interval Notation

The video tutorial explains how to solve an inequality by isolating the variable x. It involves multiplying by the reciprocal to simplify the equation, solving for x, and graphing the solution on a number line. The solution is also expressed in interval notation, showing all x values greater than 13.

What is the primary goal when solving an inequality?

• To graph the solution

• To isolate the variable x

• To eliminate all fractions

• To find the value of y

What is the reciprocal of two-fifths?

• Five over two

• Two over five

• One over five

• Five over one

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

• To add fractions

• To eliminate the fraction

• To change the inequality sign

• To simplify the variable

What happens to the twos and fives when simplifying the inequality?

• They are multiplied

• They are added

• They are subtracted

• They cancel each other out

After simplifying, what is the inequality before dividing by 2?

• 2x > 25

• 2x > 26

• x > 26

• x > 13

What is the final solution of the inequality?

• x = 13

• x > 13

• x > 12

• x < 13

What operation is performed after adding 1 to both sides of the inequality?

• Multiplication

• Division

• Subtraction

• Addition

What is the result of dividing 26 by 2 in the inequality?

• x > 12

• x > 13

• x < 13

• x = 13

How is the solution represented on a number line?

• An open circle at 13 with shading to the left

• A closed circle at 13 with shading to the left

• An open circle at 13 with shading to the right

• A closed circle at 13

What does the parentheses in the graph indicate?

• The solution includes 13

• The solution excludes 13

• The solution is equal to 13

• The solution is less than 13