Question

Write the absolute value equations in the form |x-b|=c (where b is a number and c can be either a number or an expression) that have the following solution sets. Two solutions: x=2, x=14

Answer 1

|x - 8| = 6

Explanation:

|x - b| = c

⇒ (x - b)² = c²

Given:

• x = 2
• x = 14

Substitute the values of x into (x - b)² = c²:

(2 - b)² = c²

(14 - b)² = c²

Equate and solve for b:

(2 - b)² = (14 - b)²

⇒ 4 - 4b + b² = 196 - 28b + b²

⇒ 4 - 4b = 196 - 28b

⇒ 24b = 192

⇒ b = 8

Substitute b = 8 into the equations to find c:

x = 2 ⇒ |2 - 8| = 6

x = 14 ⇒ |14 - 8| = 6

Therefore, c = 6

Final equation: |x - 8| = 6