Question

Which of the following is(are) the solutions(s) to
`| x+3 | = 7x-4`

Answer 1

B. x=7/6

Explanation:

A P E X

Answer 2

`B. \: x = (7)/(6)`

EXPLANATION

The given absolute value equation is

`|x + 3| = 7x - 4`

This implies that, either

`x + 3= 7x - 4`

Or

`- (x + 3)= 7x - 4`

`- x - 3 = 7x - 4`

Group similar terms;

`3 + 4 = 7x - x`

or

`- 3 + 4 = 7x + x`

Simplify:

`7 = 6x`

or

`1 = 8x`

Solve for x.

`x = (7)/(6) \: or \: x = (1)/(8)`

Check for extraneous solutions.

`| (7)/(6) + 3| = 7 * (7)/(6) - 4`

`(25)/(6) = (25)/(6)`

Also,

`| (1)/(8) + 3| = 7 * (1)/(8) - 4`

`(25)/(8) = - (25)/(8)`

This is an extraneous solution.

The only solution is:

`x = (7)/(6)`