Understanding Absolute Value Equations

The video tutorial explains how to solve the absolute value equation 2x - 7 = 4. It covers expressing the solution as a compound inequality, graphing it on a number line, and using interval notation. The process involves setting up two inequalities, solving them, graphing the solutions, and finding the intersection of the intervals. The final solution is expressed in interval notation, demonstrating the closed interval from 3/2 to 11/2.

What is the absolute value equation we are trying to solve?

• x - 4 = 2

• 3x - 2 = 5

• x + 5 = 3

• 2x - 7 = 4

How do we express the solution of the absolute value equation?

• Only as a graph

• As a compound inequality, a graph, and using interval notation

• Only using interval notation

• As a single inequality

What are the two inequalities derived from the absolute value equation 2x - 7 = 4?

• 2x - 7 > 4 and 2x - 7 < -4

• 2x - 7 = 4 and 2x - 7 = -4

• 2x + 7 > 4 and 2x + 7 < -4

• 2x + 7 = 4 and 2x + 7 = -4

What is the solution for x when solving 2x - 7 = 4?

• x = 5

• x = 11/2

• x = 3

• x = 7

What is the decimal equivalent of 11/2?

• 4.5

• 5.5

• 6.5

• 3.5

Where is 3/2 located on the number line?

• Between 4 and 5

• Between 3 and 4

• Between 2 and 3

• Between 1 and 2

What does the graph of x = 11/2 look like?

• An open point at 11/2 with an arrow to the left

• A closed point at 11/2 with an arrow to the left

• A closed point at 11/2 with an arrow to the right

• An open point at 11/2 with an arrow to the right

What is the intersection of the intervals for the solutions?

• Between 3/2 and 11/2

• Between 1/2 and 3/2

• Between 2 and 5

• Between 4 and 6

How is the solution expressed using interval notation?

• (1/2, 5/2)

• [3/2, 11/2]

• (3/2, 11/2)

• [1/2, 5/2]

Which of the following methods was NOT used to express the solution?

• Compound inequality

• Graph

• Interval notation

• Matrix representation