Solving Linear Inequalities in One Variable

The video tutorial explains the concept of inequalities and their application in real-life scenarios. It demonstrates solving inequalities using trial and error and introduces systematic rules for solving them, similar to linear equations. The tutorial also covers graphical representation of inequalities on a number line and solving both strict and slack linear inequalities.

What is the primary purpose of using inequalities in mathematical problems?

• To solve quadratic equations

• To find exact solutions

• To represent situations that cannot be expressed as equations

• To simplify complex equations

In the shopkeeper example, what does the inequality 40x > 200 represent?

• The number of toys needed to make a profit

• The number of toys needed to break even

• The price of each toy

• The shopkeeper's total cost

What is the solution set for the inequality 40x > 200?

• x = 5

• x > 5

• x = 6

• x < 5

Which rule is NOT applicable to inequalities?

• Adding the same number to both sides

• Dividing both sides by a positive number

• Subtracting the same number from both sides

• Multiplying both sides by a negative number without changing the inequality sign

What happens to the inequality sign when both sides are multiplied by a negative number?

• It remains unchanged

• It disappears

• It reverses

• It becomes an equation

How is the solution set for the inequality 7x + 9 > 30 represented on a number line?

• With a closed circle on 3 and an arrow to the left

• With an open circle on 3 and an arrow to the left

• With an open circle on 3 and an arrow to the right

• With a closed circle on 3 and an arrow to the right

What is the solution set for the inequality 7x + 9 > 30?

• x < 3

• x ≤ 3

• x > 3

• x = 3

In solving slack inequalities, what does a closed circle on the number line indicate?

• The inequality is strict

• The inequality is invalid

• The value is included in the solution set

• The value is not included in the solution set

What is the solution set for the inequality 2(2x + 3) - 10 ≤ 6(x - 2)?

• x ≥ 4

• x ≤ 4

• x > 4

• x < 4

What is the first step in solving a linear inequality?

• Graph the solution set

• Simplify both sides of the inequality

• Obtain the underlying linear inequality

• Divide both sides by the coefficient of the variable