6.02 Homework - 12/16/2024

Front

What does it mean if a line is dotted in an inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set of the inequality.

Front

What is the solution to the inequality -2x ≥ 22?

Back

x ≤ -11 (The sign flips when dividing by a negative number).

Front

What is the solution to the inequality m - 5 > 8?

Back

m > 13 (The sign does not flip because we are adding 5 to both sides).

Front

How do you determine if a point is a solution to an inequality?

Back

Substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the significance of the shaded region in a graph of an inequality?

Back

The shaded region represents all the solutions to the inequality.

Front

What does the inequality y < -\frac{4}{5}x - 3 represent graphically?

Back

It represents all the points below the line y = -\frac{4}{5}x - 3.

Front

What does the inequality y < -\frac{1}{2}x - 3 represent graphically?

Back

It represents all the points below the line y = -\frac{1}{2}x - 3.

Front

What happens to the inequality sign when multiplying or dividing by a negative number?

Back

The inequality sign flips.

Front

What is the general form of a linear inequality?

Back

It is typically written as ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

Front

How can you graph a linear inequality?

Back

First, graph the corresponding equation as a line, then shade the appropriate region based on the inequality.