Solving Absolute Value Equations in Algebra

The video tutorial explains how to solve an equation involving the absolute value of x. It begins by isolating the absolute value expression and simplifying the equation. The instructor then discusses the concept of absolute value, explaining that it represents the distance from zero. Two possible solutions for x are derived, verified, and graphed on a number line. The tutorial emphasizes understanding the absolute value concept and solving equations step-by-step.

What is the first step to isolate the absolute value expression in the given equation?

• Divide both sides by 5

• Subtract 3 from both sides

• Multiply both sides by 5

• Add 3 to both sides

After adding 3 to both sides, what does the equation become?

• 5|x + 3| = 4

• 5|x + 3| = 10

• 5|x + 3| = 7

• 5|x + 3| = 2

What is the next step after obtaining 5|x + 3| = 10?

• Subtract 3 from both sides

• Multiply both sides by 5

• Divide both sides by 5

• Add 3 to both sides

If the absolute value of a number is 2, what are the possible values of that number?

• 2 and -3

• 2 and -2

• 2 and 3

• 2 and 0

What equation do we get when we assume x + 3 is equal to 2?

• x + 3 = -2

• x + 3 = 0

• x + 3 = 2

• x + 3 = 3

What is the value of x when x + 3 is equal to 2?

• x = -2

• x = 2

• x = -1

• x = 1

What is the value of x when x + 3 is equal to -2?

• x = 1

• x = -1

• x = -5

• x = 5

What is the result of substituting x = -1 back into the original equation?

• 5|-2| - 3 = 7

• 5|1| - 3 = 7

• 5|0| - 3 = 7

• 5|2| - 3 = 7

What is the result of substituting x = -5 back into the original equation?

• 5|-2| - 3 = 7

• 5|1| - 3 = 7

• 5|2| - 3 = 7

• 5|0| - 3 = 7

Where would you plot the solution x = -1 on a number line?

• At 1

• At -1

• At -5

• At 5