Exploring Absolute Value Equations in Algebra

The video tutorial covers the concept of absolute values, explaining them as the distance from zero and always resulting in a positive number. It demonstrates solving equations with absolute values, showing how to interpret them as distances and solve systematically. The tutorial also explores graphing absolute value functions, illustrating how they form a v-shaped graph and discussing scenarios where the function inside the absolute value is positive or negative.

What does the absolute value of a number represent?

• The number squared

• The negative version of the number

• The positive version of the number

• The number divided by 2

How is the absolute value related to distance?

• It represents the distance from zero.

• It represents the distance between two numbers.

• It is unrelated to distance.

• It represents the distance from one.

What is the absolute value of -7,346?

• 7,346

• -7,346

• 0

• 7.346

If the absolute value of x - 5 equals 10, what could be the value of x?

• -5

• 0

• 5

• 15

For the equation |x - 5| = 10, what does x - 5 equal to?

• 10

• -10

• 5

• Both 10 and -10

For the equation |x + 2| = 6, what are the possible values of x?

• -4 and 8

• 4 and 8

• -4 and -8

• 4 and -8

In the context of absolute values, what does |x - (-2)| = 6 imply about x?

• x is 6 units away from -2

• x is 6 units away from 2

• x equals -8 or 4

• x equals 8 or -4

In the equation |4x - 1| = 19, what is one possible value of x?

• 5

• -4.5

• 4.75

• -9/2

What does the graph of y = |x + 3| look like?

• A straight line

• A U-shaped graph

• A parabola

• A V-shaped graph

When graphing y = |x + 3|, for x > -3, how does the graph behave?

• It slopes downwards.

• It slopes upwards.

• It becomes undefined.

• It remains constant.