Question

Solve |x–1| = 6x + 12

Answer 1

`x = - (11)/(7)`

Explanation:

1) Break down the problem into these 2 equations.

`x - 1 = 6x + 12`

`- (x - 1) = 6x + 12`

2) Solve the first equation. x - 1 = 6x + 12

`x = - (13)/(5)`

3) Solve the second equation: -( x - 1 ) = 6x + 12.

`x = - (11)/(7)`

4) Collect all solution.

`x = - (13)/(5). - (11)/(7)`

5) Check solution.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.

When x=-\frac{13}{5}x=−513, the original equation |x-1|=6x+12∣x−1∣=6x+12 does not hold true.We will drop x=-\frac{13}{5}x=−513 from the solution set.

6) Simplify.

`x = - (11)/(7)`

Therefor, the answer is x = - 11/7.