Solving Absolute Value Equations

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