Solving Two-Step Inequalities with Number Lines

This video tutorial by Kirk Weiler from eMathInstruction covers solving two-step inequalities. It begins with an introduction to inequalities, explaining the difference between inequalities and equations. The video then moves on to exercises that demonstrate how to determine if a value is a solution to an inequality and explores the properties of inequalities. The tutorial includes practice problems to reinforce the concepts and concludes with a preview of the next lesson, which will cover an exception to the rules discussed.

What is the main difference between an inequality and an equation?

• An inequality can have a greater than or less than symbol.

• An inequality can only have positive numbers.

• An inequality always has an equal sign.

• An inequality can only have negative numbers.

How can you determine if a value is a solution to an inequality?

• By multiplying the value by both sides of the inequality.

• By subtracting the value from both sides of the inequality.

• By adding the value to both sides of the inequality.

• By plugging the value into the inequality and checking if it makes the inequality true.

What happens to an inequality when you add the same number to both sides?

• The inequality changes direction.

• The inequality becomes an equation.

• The inequality remains true.

• The inequality becomes false.

What is the result of multiplying both sides of the inequality 10 > 4 by 3?

• 30 < 12

• 10 < 12

• 30 > 12

• 10 > 12

How do you solve the inequality 3x + 5 > 17?

• Subtract 5 from both sides, then divide by 3.

• Divide both sides by 3, then add 5.

• Multiply both sides by 3, then subtract 5.

• Add 5 to both sides, then divide by 3.

What does the solution x > 4 mean in terms of graphing on a number line?

• Shade only the number 4.

• Shade all numbers to the right of 4, excluding 4.

• Shade all numbers to the right of 4, including 4.

• Shade all numbers to the left of 4.

In the inequality 2x - 9 ≤ 3, what is the first step to isolate x?

• Add 9 to both sides.

• Divide both sides by 2.

• Subtract 9 from both sides.

• Multiply both sides by 2.

What is the solution to the inequality 3/2x + 11 > 5?

• x < 4

• x > -4

• x < -4

• x > 4

How do you graph the solution n < 8 on a number line?

• Fill in 8 and shade to the left.

• Fill in 8 and shade to the right.

• Circle 8 and shade to the right.

• Circle 8 and shade to the left.

What is the solution to the inequality 5c + 7 ≥ 2?

• c ≥ -1

• c ≤ -1

• c ≥ 1

• c ≤ 1