Solving Linear and Absolute Value Equations

The video tutorial explains absolute value functions, starting with a basic introduction using a number line to illustrate the concept. It then moves on to solving absolute value equations, demonstrating the process with examples. The tutorial covers both positive and negative scenarios, showing how to solve for x in each case. The video concludes with a detailed example problem, highlighting the steps to find solutions that satisfy the absolute value equation.

What is the best way to understand an absolute value function?

• By looking at a graph

• By using a number line

• By using a calculator

• By solving equations

If the absolute value of -3 is calculated, what is the result?

• -3

• 0

• 6

• 3

What does the absolute value of a number represent?

• The number itself

• The distance from zero on a number line

• The negative of the number

• The square of the number

When solving an absolute value equation, why do we consider both positive and negative solutions?

• Because absolute value can be either positive or negative

• Because the distance can be in any direction

• Because we need to check for errors

• Because it simplifies the equation

What is the first step in solving the equation x + 10 = 4x - 8?

• Add 10 to both sides

• Divide both sides by 2

• Subtract x from both sides

• Multiply both sides by 4

After subtracting x from both sides in the equation x + 10 = 4x - 8, what is the resulting equation?

• 10 = 3x - 8

• 10 = 4x - 8

• x = 3x - 8

• x = 4x - 8

What is the value of x when solving 10 = 3x - 8?

• x = 2

• x = 4

• x = 6

• x = 8

In the equation x + 10 = -4x + 8, what is the first step after distributing the negative sign?

• Add x to both sides

• Subtract x from both sides

• Add 10 to both sides

• Subtract 8 from both sides

What is the value of x when solving 2 = -x?

• x = -1

• x = -2

• x = 1

• x = 2

What do the solutions x = 6 and x = -2/5 represent in the context of the absolute value function?

• They are approximate solutions

• They are incorrect solutions

• They are the only possible solutions

• They satisfy the absolute value equation