Question

Solve for x: 1/7 (x - 3) - 2 = 9

A. x = 74 and x = 80
B. x = -46 and x =52
C. x = -52 and x = 46
D. x= -74 and x = 80

Answer 1

x = 80

Step-by-step explanation:

`(1)/(7)` (x - 3) - 2 = 9 ( add 2 to both sides )

`(1)/(7)` (x - 3) = 11 ( multiply both sides by 7 to clear the fraction )

x - 3 = 77 ( add 3 to both sides )

x = 80 ← is the only solution

Answer 2

D. x= -74 and x = 80

Step-by-step explanation:

`\sf \rightarrow (1)/(7) |x-3| -2 = 9`

`\sf \rightarrow (1)/(7) |x-3| = 9 + 2`

`\sf \rightarrow (1)/(7) |x-3| = 11`

`\sf \rightarrow |x-3| = 11 * 7`

`\sf \rightarrow |x-3| =77`

`\sf \rightarrow x-3= \pm 77`

`\sf \rightarrow x-3= 77 \quad or \quad x - 3 = -77`

`\sf \rightarrow x= 77+3 \quad or \quad x = -77+3`

`\sf \rightarrow x= 80 \quad or \quad x = -74`