12.03 Warm-Up

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you split an absolute value inequality like |x + 5| < 10 into two inequalities?

Back

You split it into two inequalities: x + 5 < 10 and x + 5 > -10.

Front

What does it mean if a line in a graph is dotted?

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 -3(3x + 5) > -5(2x - 2)?

Back

The solution is x > 25.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + b < c, ax + b > c, etc.

Front

How do you graph a linear inequality like y > (1/2)x + 3?

Back

Graph the line y = (1/2)x + 3 as a dotted line and shade the region above the line.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means greater than and does not include the boundary, while '≥' means greater than or equal to and includes the boundary.

Front

What does it mean for a point to be a solution to an inequality?

Back

A point is a solution to an inequality if it satisfies the inequality when substituted into it.

Front

How do you determine if a point (3, 1) is a solution to the inequality y < (1/2)x + 3?

Back

Substitute x = 3 into the inequality: 1 < (1/2)(3) + 3. If true, (3, 1) is a solution.

Front

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

Back

The shaded region represents all the possible solutions to the inequality.