Solving Linear Inequalities

The video tutorial covers solving one-step inequalities using inverse operations and graphing. It includes eight examples, each demonstrating how to isolate variables and verify solutions through graphing. The tutorial emphasizes understanding equivalent inequalities and checking solutions for accuracy.

What is the first step in solving one-step inequalities?

• Add a constant to both sides

• Multiply both sides by zero

• Graph the inequality

• Isolate the variable using inverse operations

In the inequality x + 5 ≥ 12, what operation should be performed to isolate x?

• Subtract 5 from both sides

• Add 5 to both sides

• Divide both sides by 5

• Multiply both sides by 5

When graphing x ≥ 7, what type of circle is used on the number line?

• No circle

• Dashed circle

• Closed circle

• Open circle

For the inequality 5 > x - 4, what is the inverse operation to solve for x?

• Multiply both sides by 4

• Subtract 4 from both sides

• Add 4 to both sides

• Divide both sides by 4

In the inequality 9 > x, which direction does the arrow point on the number line?

• No direction

• Both directions

• Towards lesser values

• Towards greater values

How do you solve 3x ≤ 12?

• Multiply both sides by 3

• Subtract 3 from both sides

• Add 3 to both sides

• Divide both sides by 3

What is the solution to the inequality 3x ≤ 12?

• x < 4

• x > 4

• x ≥ 4

• x ≤ 4

In the inequality x/6 < 4, what operation is used to solve for x?

• Add 6 to both sides

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 6 from both sides

What is the boundary value when graphing x < 24?

• 26

• 25

• 24

• 23

How do you solve 7 ≤ x + 5?

• Multiply both sides by 5

• Subtract 5 from both sides

• Divide both sides by 5

• Add 5 to both sides