Solving Absolute Value Equations

This video tutorial covers the topic of absolute value equations, explaining how to solve them by splitting into positive and negative cases. It provides multiple examples, each with step-by-step solutions, highlighting the importance of isolating the absolute value part before solving. The tutorial also addresses common misconceptions and emphasizes the necessity of showing all work. The video concludes with a brief mention of the next topic, absolute value inequalities.

What is the first step in solving an absolute value equation?

• Combine like terms

• Isolate the absolute value part

• Multiply both sides by a constant

• Add a constant to both sides

Why do we split an absolute value equation into two separate equations?

• To isolate the variable

• To account for both positive and negative solutions

• To simplify the equation

• To eliminate the absolute value

In Example 1, what is the first step to isolate the absolute value part?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3

What are the solutions for the equation |x - 3| = 10?

• x = 10 or x = -10

• x = 13 or x = -7

• x = 7 or x = -13

• x = 10 or x = 3

In Example 2, what is the next step after splitting the equation |x + 4| = 6 into two cases?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide both sides by 4

• Multiply both sides by 4

What are the solutions for the equation |x + 4| = 6?

• x = 6 or x = -6

• x = 10 or x = -2

• x = 2 or x = -10

• x = 2 or x = -2

In Example 3, what is the first step to isolate the absolute value part in the equation |x - 3| + 2 = 10?

• Divide both sides by 2

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply both sides by 2

What are the solutions for the equation |x - 3| = 8?

• x = 3 or x = -3

• x = 8 or x = -8

• x = 5 or x = -11

• x = 11 or x = -5

In Example 5, what is the first step to isolate the absolute value part in the equation 2|x - 1| = 8?

• Divide both sides by 2

• Add 2 to both sides

• Multiply both sides by 2

• Subtract 2 from both sides

What are the solutions for the equation |2x + 1| = 16?

• x = 8 or x = -8

• x = 15/2 or x = -17/2

• x = 16 or x = -16

• x = 2 or x = -2