Mastering Multi-Step Inequalities

Maria, a mathematician, explains how to solve multi-step inequalities using the DCI method: Distribute, Combine, and Inverse operations. She demonstrates solving the inequality -2(x + 3) ≥ 10 by distributing, combining like terms, and using inverse operations to isolate x. Maria highlights the importance of flipping the inequality sign when dividing by a negative number. Finally, she shows how to graph the solution, emphasizing shading and direction based on the inequality.

What is the first step in solving the given multi-step inequality?

• Divide by negative two

• Add six to both sides

• Combine like terms

• Distribute the negative two

What does the acronym DC I stand for?

• Distribute, Combine, Inverse

• Divide, Combine, Isolate

• Distribute, Calculate, Inverse

• Divide, Calculate, Isolate

What is the result of distributing negative two to the terms inside the parenthesis?

• 2x + 6

• 2x - 6

• -2x + 6

• -2x - 6

After distributing, what is the next step according to the DC I method?

• Isolate the variable

• Combine like terms

• Add six to both sides

• Divide by negative two

Why do we add six to both sides of the inequality?

• To combine like terms

• To get rid of the negative sign

• To isolate the variable

• To balance the equation

What is the result of adding six to both sides of the inequality?

• -2x ≥ 16

• -2x ≥ 10

• -2x ≤ 16

• -2x = 16

What operation is used to isolate the variable x after adding six to both sides?

• Subtraction

• Division

• Addition

• Multiplication

What important rule must be followed when dividing by a negative number in an inequality?

• The inequality sign stays the same

• The inequality sign flips

• The variable must be negative

• The variable must be positive

What is the final solution to the inequality after all steps are completed?

• x ≤ -8

• x < -8

• x > -8

• x ≥ -8

When graphing the solution, which direction do you shade on the number line?

• Both sides of -8

• To the left of -8

• To the right of -8

• Do not shade