Inequalities and Their Solutions

The video tutorial demonstrates solving inequalities with variables on both sides. It emphasizes treating inequalities like equations, with special attention to operations involving negative numbers. Two example problems are solved: 5 + 2m < -3m and 2(5-x) < 3x. The tutorial highlights the importance of obtaining positive variable terms to simplify the process and avoid extra steps like flipping the inequality sign. Graphing solutions is also covered.

What is the key consideration when solving inequalities with variables on both sides?

• Treat them as equations and be cautious with negative numbers.

• Always add variables to the right side.

• Ignore the negative numbers.

• Multiply all terms by zero.

What happens if you divide or multiply by a negative number in an inequality?

• The inequality becomes an equation.

• The inequality sign flips.

• The inequality sign stays the same.

• The inequality becomes invalid.

In the inequality 5 + 2m < -3m, which variable term should be moved to achieve a positive result?

• Move -3m to the right.

• Move -3m to the left.

• Move 2m to the right.

• Move 5 to the right.

In the inequality 5 + 2m < -3m, what operation is performed to move -3m?

• Multiply both sides by 3.

• Divide both sides by 3.

• Subtract 3m from both sides.

• Add 3m to both sides.

After moving the variable terms in the inequality 5 + 2m < -3m, what is the resulting inequality?

• 5 + 2m < 0

• 5 - 5m < 0

• 5 + 5m < 0

• 5 - 2m < 0

What is the solution to the inequality 5 + 5m < 0?

• m < 1

• m > 1

• m < -1

• m > -1

How is the solution m < -1 represented on a number line?

• Open circle on -1, arrow to the left.

• Open circle on 1, arrow to the right.

• Closed circle on 1, arrow to the left.

• Closed circle on -1, arrow to the right.

What is the result of dividing both sides of the inequality 5m < -5 by 5?

• m < 1

• m > -1

• m < -1

• m > 1

In the inequality 2(5 - x) < 3x, what is the first step to simplify it?

• Distribute the 2 across the terms inside the parentheses.

• Add 3x to both sides.

• Multiply both sides by 2.

• Subtract 5 from both sides.

After distributing in the inequality 2(5 - x) < 3x, what is the resulting inequality?

• 10 - 2x < 3x

• 5 + 2x < 3x

• 10 + 2x < 3x

• 5 - 2x < 3x