Understanding Inequalities

The video tutorial explains how to solve inequalities, emphasizing the key rule of reversing the inequality symbol when multiplying or dividing by a negative number. It demonstrates clearing fractions, simplifying expressions, isolating variables, and solving the inequality. The solution is then represented graphically and in interval notation.

What is the key difference between solving an equation and an inequality?

• Inequalities do not have solutions.

• You cannot subtract numbers from both sides in an inequality.

• You must reverse the inequality symbol when multiplying or dividing by a negative.

• You can add numbers to both sides in an inequality.

Why do we multiply both sides of the inequality by four in the first step?

• To make the inequality more complex.

• To clear the fraction from the inequality.

• To add more variables to the inequality.

• To reverse the inequality symbol.

What is the result of distributing negative one in the expression?

• It changes the sign of each term inside the parentheses.

• It reverses the inequality symbol.

• It makes all terms positive.

• It adds a constant to the inequality.

How do you isolate the variable term in the inequality?

• By adding or subtracting terms from both sides.

• By reversing the inequality symbol.

• By adding more variables to the inequality.

• By multiplying the variable by zero.

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

• The inequality symbol remains the same.

• The inequality becomes an equation.

• The inequality symbol must be reversed.

• The variable becomes zero.

What does the solution M > -4 mean on a number line?

• M is less than -4.

• M is greater than or equal to -4.

• M is equal to -4.

• M is greater than -4, represented by an open circle at -4 and an arrow to the right.

How is the interval notation for M > -4 written?

• (-∞, -4]

• [4, ∞)

• [-4, ∞)

• (-4, ∞)

What does an open circle on a number line indicate?

• The solution is incorrect.

• The number is not included in the solution.

• The number is included in the solution.

• The inequality symbol is reversed.

Why do we use rounded parentheses in interval notation?

• To indicate that the endpoint is included.

• To indicate that the endpoint is not included.

• To denote a closed interval.

• To show that the interval is finite.

What is the significance of the arrow direction in the graph of M > -4?

• It indicates the values greater than -4.

• It shows the values equal to -4.

• It shows the values less than -4.

• It points to the solution being incorrect.