Solving Inequalities with Multiplication and Division

The video tutorial covers solving inequalities using multiplication and division. It explains the multiplication property of equality and how it applies to inequalities. The tutorial highlights the importance of flipping the inequality sign when multiplying or dividing by a negative number. Several examples are provided to illustrate these concepts, including solving and graphing inequalities on a number line.

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

• It doubles.

• It remains unchanged.

• It disappears.

• It flips.

If -4x < 28, what is the correct operation to solve for x?

• Divide both sides by 4.

• Multiply both sides by -4.

• Divide both sides by -4.

• Multiply both sides by 4.

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Nothing changes.

• Flip the inequality sign.

• Add 1 to both sides.

• Subtract 1 from both sides.

When graphing x > -7, what symbol is used on the number line?

• An open dot.

• A square.

• A cross.

• A filled dot.

When solving inequalities, why is it necessary to flip the inequality sign under certain conditions?

• To make both sides positive.

• It's a mathematical convention without reason.

• To maintain the original value relationship.

• To simplify the inequality.

If dividing by a positive number, does the inequality sign flip?

• Yes, always.

• No, it remains the same.

• Yes, but only in special cases.

• It depends on the value of the number.

What is the result of dividing both sides of -30 ≥ 3x by 3?

• -10 ≥ x

• x ≥ -10

• x ≤ -10

• -10 ≤ x

How do you graph x ≥ 40 on a number line?

• With an open dot pointing left.

• With an open dot pointing right.

• With a filled dot pointing right.

• With a filled dot pointing left.

What is the correct graph symbol for x ≤ -10?

• A filled dot pointing right.

• A filled dot pointing left.

• An open dot pointing right.

• An open dot pointing left.

If x/(-4) ≤ -10, after moving the negative to the denominator, what is the next step?

• Divide both sides by 4 and flip the sign.

• Multiply both sides by 4 and keep the sign.

• Divide both sides by -4 and keep the sign.

• Multiply both sides by -4 and flip the sign.