Systems of Inequalities

Front

What type of line is used for inequalities with \( \ge \) or \( \le \)?

Back

Solid line

Front

What type of line is used for inequalities with \( > \) or \( < \)?

Back

Dotted line

Front

How do you represent the inequality \( x \ge 5 \) on a graph?

Back

A solid vertical line at \( x = 5 \) with shading to the right.

Front

What does the solution to a system of inequalities represent?

Back

The region where the shaded areas of all inequalities overlap.

Front

How do you graph the inequality \( y < \frac{1}{2}x - 1 \)?

Back

Graph the line \( y = \frac{1}{2}x - 1 \) as a dotted line and shade below it.

Front

What is the first step in solving a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane.

Front

What does the symbol \( \ge \) indicate in an inequality?

Back

It indicates that the value is greater than or equal to.

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates inclusion (\( \ge \) or \( \le \)), while a dotted line indicates exclusion (\( > \) or \( < \)).

Front

How do you determine the feasible region in a system of inequalities?

Back

By finding the intersection of the shaded regions of all inequalities.

Front

What is the graphical representation of the inequality \( y \ge -3x + 4 \)?

Back

A solid line for \( y = -3x + 4 \) with shading above the line.