Understanding and Solving Inequalities

The video tutorial explains how to solve an inequality involving decimals by first clearing the decimals through multiplication. It then guides through distributing and simplifying the inequality, solving it while reversing the inequality symbol when necessary. Finally, it demonstrates how to graph the solution on a number line and express it using interval notation.

What is the first step in solving an inequality that contains decimals?

• Divide both sides by 10

• Subtract the decimals from both sides

• Multiply both sides by 10

• Add the decimals to both sides

When multiplying by 10, what happens to the decimal point?

• It moves two places to the left

• It disappears

• It stays in the same place

• It moves one place to the right

What must you remember to do when multiplying or dividing both sides of an inequality by a negative number?

• Subtract 1 from both sides

• Add 1 to both sides

• Reverse the inequality symbol

• Keep the inequality symbol the same

What is the result of dividing -8 by -1 in the inequality?

• 1

• 0

• -8

• 8

What does the inequality x < -8 imply about the values of x?

• x is greater than -8

• x is equal to -8

• x is less than -8

• x is not a real number

How is the solution x < -8 represented on a number line?

• A closed point on -8 with shading to the right

• An open point on -8 with shading to the left

• A closed point on -8 with shading to the left

• An open point on -8 with shading to the right

What is the purpose of graphing the solution on a number line?

• To visualize the solution set

• To check the solution

• To find the exact value of x

• To solve the inequality

What does an open interval mean in interval notation?

• The interval includes only the right endpoint

• The interval includes only the left endpoint

• The interval does not include either endpoint

• The interval includes both endpoints

What is the interval notation for the solution x < -8?

• (-∞, -8]

• (-8, ∞)

• (-∞, -8)

• [-8, ∞)

Why do we use parentheses in interval notation for x < -8?

• Because -8 is not included in the interval

• Because -8 is included in the interval

• Because the interval is infinite

• Because the interval is finite