Solving and Interpreting Inequalities

The video tutorial explains how to solve the inequality 15 ≥ 3 * 4x - 7 by isolating the variable X. The process involves dividing both sides by three, using the additive property to eliminate constants, and finally dividing by four to solve for X. The solution shows that X must be less than or equal to three for the inequality to hold true.

What is the main objective when solving the inequality 15 ≥ 3 * 4x - 7?

• To find the value of 15

• To determine the values of X that satisfy the inequality

• To simplify the expression 3 * 4x - 7

• To prove that 15 is always greater than 3 * 4x - 7

What is the first step taken to simplify the inequality 15 ≥ 3 * 4x - 7?

• Add 7 to both sides

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 7 from both sides

Why does the inequality sign remain unchanged when dividing both sides by 3?

• Because 3 is a positive number

• Because the inequality is already balanced

• Because 15 is greater than 3

• Because division always keeps the sign the same

What operation is used to eliminate the -7 in the inequality 5 ≥ 4x - 7?

• Multiplication

• Division

• Subtraction

• Addition

After adding 7 to both sides, what does the inequality become?

• 12 ≥ 4x

• 5 ≥ 4x

• 5 ≥ 4x - 7

• 12 ≥ 4x - 7

What is the final step to solve the inequality 12 ≥ 4x?

• Add 4 to both sides

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 4 from both sides

What is the solution to the inequality 12 ≥ 4x after dividing by 4?

• x < 3

• x = 3

• x ≥ 3

• x ≤ 3

Why is it important to note that the division was not by a negative number?

• Because it simplifies the calculation

• Because it would require flipping the inequality sign

• Because it makes the inequality invalid

• Because it changes the inequality to an equation

How can the final inequality 3 ≥ x be interpreted?

• X is greater than or equal to 3

• X is less than or equal to 3

• X is equal to 3

• X is greater than 3

What does the inequality 3 ≥ x imply about the possible values of X?

• X can be any number greater than 3

• X can only be 3

• X can be any number less than or equal to 3

• X can be any number