Solving Inequalities and Graphing

The video tutorial covers solving and graphing two-part inequalities for grade 7 math. It explains the multiplication and division properties of inequalities, emphasizing the need to reverse the inequality sign when multiplying or dividing by a negative number. The tutorial provides step-by-step examples of solving inequalities and graphing them on a number line, including how to handle cases where a variable is not equal to a specific value.

What is the first step in solving a two-part inequality?

• Subtract a constant from both sides

• Add a constant to both sides

• Graph the inequality

• Multiply both sides by a constant

What happens to the inequality sign when you multiply or divide both sides by a negative number?

• It becomes an equal sign

• It disappears

• It stays the same

• It reverses direction

In the example where 3x is on one side and 15 on the other, what operation is used to isolate x?

• Subtraction

• Addition

• Multiplication

• Division

What is the solution to the inequality 3x < 15?

• x ≥ 5

• x = 5

• x < 5

• x > 5

In the inequality 10 - 0.75p ≤ 7, what is the first step to solve it?

• Divide both sides by 0.75

• Multiply both sides by 0.75

• Subtract 10 from both sides

• Add 10 to both sides

What is the solution to the inequality 10 - 0.75p ≤ 7 after solving?

• p ≥ 4

• p ≤ 4

• p > 4

• p < 4

When graphing p ≥ 4, what type of dot is used to indicate that 4 is included?

• Filled black dot

• Open circle

• Cross

• Triangle

Why do we reverse the inequality sign when dividing by a negative number?

• To simplify the graph

• To eliminate the variable

• To keep the statement true

• To make the equation easier

In the inequality -8y + 4 ≥ 0, what is the first step to solve it?

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 8

• Divide both sides by 8

What is the solution to the inequality -8y + 4 ≥ 0 after solving?

• y ≤ 0.5

• y > 0.5

• y ≥ 0.5

• y < 0.5