Inequalities and Sign Changes

The video tutorial explains how to solve the inequality -2x + 1 ≤ 7. It begins by treating the inequality like an equation, emphasizing the importance of changing the inequality sign when multiplying or dividing by a negative number. The process involves subtracting 1 from both sides, resulting in -2x ≤ 6. Then, dividing both sides by -2 changes the inequality direction, leading to the solution x ≥ -3, which corresponds to answer choice D.

When solving inequalities, what must you do if you multiply or divide by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Keep the inequality sign the same

• Change the direction of the inequality sign

What is the key concept to remember when solving inequalities?

• Always subtract from both sides

• Keep the inequality sign the same

• Change the inequality sign when multiplying or dividing by a negative

• Always add to both sides

What is the key concept to remember when solving inequalities?

• Keep the inequality sign the same

• Always subtract from both sides

• Always add to both sides

• Change the inequality sign when multiplying or dividing by a negative

What is the first step in solving the inequality -2x + 1 ≤ 7?

• Divide both sides by -2

• Multiply both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

After subtracting 1 from both sides of the inequality -2x + 1 ≤ 7, what is the resulting inequality?

• -2x ≤ 8

• -2x ≤ 5

• -2x ≤ 6

• -2x ≤ 7

What is the first operation performed in solving the inequality -2x + 1 ≤ 7?

• Subtract 1 from both sides

• Multiply both sides by 2

• Divide both sides by 2

• Add 1 to both sides

What is the result of subtracting 1 from both sides of the inequality -2x + 1 ≤ 7?

• -2x ≤ 6

• -2x ≤ 5

• -2x ≤ 7

• -2x ≤ 8

What is the result of dividing both sides of the inequality -2x ≤ 6 by -2?

• x ≤ -3

• x ≥ -3

• x ≤ 3

• x ≥ 3

What is the correct answer choice for the inequality solution x ≥ -3?

• Choice A

• Choice B

• Choice C

• Choice D

What operation is performed after subtracting 1 from both sides in the inequality -2x + 1 ≤ 7?

• Multiply both sides by -2

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by -2